Her charged attack has higher scaling than Hu Tao's.
Her E with a passive can increase Rosaria's crit rate by 12%.
Her Q with a passive can give 15% of Rosaria's crit rate to others. The Q can snapshot. It pulses once every 2s. At C0 it pulses 4 times over the course of 8s. It does aoe damage within a fixed area of radius 6-6.5m (larger aoe than Xiangling).
Her C2 is the main upgrade to her burst dps. It extends her q by 4s, to a total of 12s. The lance will pulse 6 times then compared to 4 at C0. This means a dps increase of 1.5 times on the burst.
Her C1 is for a dps Rosaria build. C4 is for energy. C5 gives +3 levels to q, C3 gives +3 levels to e. Her C6 is useful for physical teams (such as with Eula).
4 piece Noblesse, 4 piece Blizzard, 4 piece berserker (for crit rate), even 4 piece Emblem for extra burst damage, or combinations of these
Noblesse and Emblem are for increasing burst dmg. Generally, Emblem will give more burst dmg, whereas Noblesse can give better support to other team members. Noblesse 2 piece gives 20% burst damage (2 noblesse-2 blizzard gives up to 35% on Rosaria's burst). Emblem 4 piece gives 25% of ER as burst damage (200% ER gives 50% burst dmg). The Noblesse 4 piece atk bonus does not stack, so if your team already has a 4 piece noblesse user, one can opt for 4p emblem (for most possible burst damage) or 2 noblesse 2 blizzard. The Blizzard set is for freeze teams and a cryo Rosaria build (say with Chongyun).
Usually want to stack crit rate or have a crit rate helmet
Weapons: CRIT rate weapons like the PJWS, ER weapons are also ok, the dragonspine spear is ok for a physical dps build
Usually used on freeze teams, as a crit rate buffer, a sub-dps on melt teams, or as a cryo battery on Eula teams
Shenhe is basically an upgrade from Rosaria except Shenhe's burst costs more (80 vs 60), Rosaria is a bit better as a cryo battery, and Rosaria buffs crit rate for everybody, not just cryo. Nonetheless, both Shenhe and Rosaria are good.
Assume C6 Rosaria with Cryo dmg goblet and 2 noblesse 2 blizzard for $$46.6+35 = 81.6$$ dmg bonus on her burst. At level 10, Rosaria's E does 2 hits with scaling \(105.12+244.8\) and cd 6s giving mv $$x_e(C0) = (105.12+244.8)*(1.466)/6 = 85.49712$$ At level 13 it is $$x_e(C3) = (124.1+289)*(1.466)/6 = 100.9341$$ At level 13 with C2, Rosaria's Q has 2 initial hits and pulses 6 times (once every 2s), with a 15s cd. The mv is $$x_q = (221+323+280.5*6)*1.816/15 = 269.615$$ In total her dps is $$x = x_e + x_q = 370.5491$$
We can redo the whole computation this time considering 4 piece emblem with 200% ER, giving 50% burst dmg, as we computed for Xiangling. For example, give Rosaria the Catch to increase her ER. The total dmg bonus becomes 96.6% this time, meaning a relative increase of \(1.966/1.816 = 1.0825991189\) times on her q. Her total dps is $$x_e + 1.0826x_q = 392.819299$$ which is quite good, comparable to Xiangling's q dps actually. And this is not considering the crit rate buffs that Rosaria has. It is also not considering any melts on her burst (which would put her dps ahead of Xiangling) or any damage from Rosaria's normal attacks (if one chooses to user her as a dps).
Suppose Rosaria has 100% crit rate, so her Q gives 15% to party members. The expected damage is proportional to $$1+rd$$ so Rosaria would increase this to $$1+rd+.15d$$ meaning damage is multiplied by $$f(r, d) = 1 + \frac{.15d}{1 + rd} = 1 + \frac{.15}{1/d + r} \le 1 + \frac{.15}{r}$$ This function increases as the crit damage d increases and as the initial crit rate r goes to 0. Theoretically, this function has no bound if we consider 0% cr and stack cd to infinity. However, by default for most characters the base crit rate \(r \ge .05\). This means theoretically (if one has infinite crit damage), Rosaria's buff can multiply damage by \(1+.15/.05 = 4\) times, which is too broken to be true.
However, getting infinite crit damage d is impossible. A well built character can attain around \(d = 2\) or 200% crit dmg, sometimes higher even reaching 300% crit dmg (but rarely higher than this). The average player can probably attain 120-160% crit damage for most characters with some work. For simplicity, we will consider an upper estimate of 200% crit dmg. This means Rosaria's buff can multiply damage by at most $$ 1+.15/(1/2+.05) \approx 1.27 $$ for characters with 200% crit damage, which is pretty good (comparable to vv buff). If the character has less than 200% crit dmg, the multiplier is smaller. If the character has more than 200% crit dmg, the multiplier is bigger. The base crit dmg for most characters is \(d \ge .5 \) so the multiplier in this case will be $$f_m = 1 + \frac{.15}{2+r} \le 1.075$$
To be fair, this is a bit deceptive. This multiplier is comparing with the situation where we start with 5% crit rate, which is too low for most characters to be competitive. To compare with other more realistic competitive teams, we should compare the effect of the crit rate bonus with a 'normal' team with decent crit rate stats. Some characters like Xiao, Yoimiya, Diluc, Itto ascend with crit rate, getting around 20% just from ascension, so they also have an inherent crit rate boost, rather than just the bare 5%. Many characters will gain crit rate from artifacts or weapons, with a crit rate helmet giving around 30% crit rate.
We suppose an average decently built character has around 50% crit rate so that Rosaria's buff becomes $$f = 1 + \frac{.15}{1/d + .5} \le 1.3$$ The higher the crit damage, the closer one gets to the bound of 1.3. For 200% crit dmg \(d=2\), the multiplier is 1.15.
But we can also reinvest that extra crit rate into more crit damage to get a higher multiplier. That is we can opt to build the character with less initial crit rate and more initial crit damage. $$f = \frac{1 + r'd'}{1 + rd}$$ where we assume that we can reinvest 1 point of crit rate into 2 points of crit dmg by reshuffling artifacts, etc. (based on distribution of stats the game provides) $$cv = 2r'+d' = 2(r+.15)+d = 2r + d + .3$$ The above is sometimes called the crit value (cv). We seek to maximize f wrt the above constraint. Define the lagrangian as $$L = r'd' + \lambda(2r'+d')$$ Taking derivatives $$\begin{align} \partial_{r'}L &= d' + 2\lambda \\ \partial_{d'}L &= r' + \lambda \end{align}$$ Solving gives $$d' = 2r'$$ In other words, we reinvest the crit rate so that we get a 1:2 ratio between crit rate and crit dmg. If we initially have a 1:2 ratio \(d = 2r\) then we re-distribute the crit rate and crit dmg as follows: $$\begin{align} d' &= 2r' \\ d + 2x &= 2(r + .15-x) \\ x &= .3/4 = 0.075 \end{align}$$ That is build the character with 15% more crit dmg and 7.5% less crit rate as the base value. Rosaria will then give 15% crit rate so that effectively we have 7.5% extra crit rate from the base. The multiplier is then $$f = \frac{1 + r'd'}{1 + rd} = \frac{1+2(r')^2}{1+2r^2} = \frac{1+2(r+.075)^2}{1+2r^2} = 1 + \frac{.15r+.075^2}{1+2r^2}$$ The max of the function occurs when $$\partial_r f = 0$$ This can be solved to give an exact result. From a graph, the function f takes a maximum of a bit more than 1.1 when crit rate is a bit more than 50%. So Rosaria's buff can multiply damage by 1.1 times (a 10% multiplicative increase through the expected crit multiplier).
This is an independent multiplier, so it is multiplicative with RES shred, DEF shred, melt/vaporize, etc.
Note this analysis assumes that we are optimizing the crit ratio. Note that the regime where the multiplier is maximized is when crit rate is around 50%. But then based on the premise of this argument, crit dmg will be around 100%. In practice, we usually have more skewed ratios for cr and cd. Crit rate may be 60% whereas crit dmg may be around 200%. Moreover, the crit rate buff does nothing as we approach the upper limit for crit rate of 100%. In this case, the analysis for the practical bound in the previous section becomes more relevant.
Lastly the above analysis assumes Rosaria has 100% crit rate so she can give 15% crit rate to others. In practice, this may be less as attaining 100% crit rate is non-trivial without proper investment.
In conclusion, the crit rate buff becomes most useful for characters who already have high crit dmg and are lacking in crit rate. For a decently invested build (around 50-60% cr), one can expect Rosaria's buff to multiply damage by 1.1 to 1.15 times.
This analysis also applies for crit dmg boosts such as from Sara, Itto, Gorou, and Shenhe. The bound of 1.1 can be achieved with an 85-230 ratio after shuffling from a 100-200 ratio. Then \(3.3/3 = 1.1\). The crit multiplier in a very good scenario will triple the damage with a 100-200 ratio.
The 1:2 optimization rule of thumb stays relevant until we get to the regime of near 100% crit rate (the boundary). Consider the case of 100-200 ratio, which gives a multiplier of 3. If we deviate from the 1:2 ratio with say crit rate r. Then having crit dmg 2/r will result in the same damage as having a perfect 100-200 ratio. For example, if one has 90% crit rate, having 222.2% or more crit dmg can become more optimal than 100-200. If one has 80% cr, having 250% or more cd can be more optimal. If one has 70% cr, one needs 286% or more cd to offset the loss in cr, and here things start becoming less feasible. If one has 60% cr, one needs 333.3% or more cd to be more optimal than 100-200. And getting more than 300% cd is not a trivial task, even for whales. So for the average player, following the 1:2 rule of thumb is useful until one starts reaching 80% cr and above. At that point, it can become more practical to maximize the product rd via stacking crit dmg.