Yelan is a hydro bow 5 star that released alongside Xiao in 2.7. Based on her kit, she appears to be a cross between Ganyu and Xingqiu. Her CA is similar to Ganyu's, and her Q is similar to Xingqiu's.
Most of her damage scales with her max HP: her breakthrough CA, E skill, and Q burst.
When spending 5s out of combat she obtains the breakthrough effect, reducing CA time by 80% and allowing her to do an aoe CA similar to Ganyu. The breakthrough aoe CA damage scales with HP. Her normal CA scales with ATK. Using her E can also help her gain breakthrough.
Her NA and PA scale with ATK. While NA she kicks her bow (who does that?).
Note her aoe CA can vaporize (2x damage), whereas Ganyu's CA can only melt (1.5x damage).
Her skill allows her to dash and tag enemies with a string (lifeline). Tagged enemies will then be damaged and knockbacked a certain degree. Each tagged enemy gives 33% chance for Yelan to obtain the breakthrough effect (allowing special aoe CA). If there are n enemies the probability of obtaining breakthrough is about $$1-(1-1/3)^n = 1 - (2/3)^n$$ In other words it increases with n. Her E has a 10s cd, which is much shorter than Xingqiu's 18s cd. Yelan's E is generally better against mobs and in aoe situations than Xingqiu's E.
Her burst is similar to Xingqiu's. She does an initial aoe hit of hydro and summons a dice (exquisite throw). The dice will shoot out 3 arrows upon NA or Yelan E. All Q damage scales with Yelan's max HP. It lasts 15s, has a cd of 18s, energy cost of 70, so it is cheaper than Xingqiu's burst (80 energy).
But wait, if her damage scales with HP, does that mean she does not get Bennett's ATK buff? Yes that's true, but Genshin actually made her HP scalings high enough to compensate for that fact. That makes her very flexible on teams that do not need Bennett (or if Bennett is on your other abyss team).
One passive boosts her HP depending on how many different element characters are in the party (similar to Yun Jin's passive). Another passive increases the active character's dmg bonus while her Q is active (starts at 1%, goes to 50%, increasing 3.5% every second).
In retrospect, this 'diversity' passive makes Yelan benefit from dendro teams, specifically hyperbloom, which requires at least 3 different elements (hydro, dendro, electro).
For a comparison between Yelan and Xingqiu: C0 Yelan is obviously better than C0-C5 Xingqiu. You really want to compare C0 Yelan with C6 Xingqiu.
Yelan will typically do more damage and provide more offensive support to the team, whereas Xingqiu can provide some more defensive support (rainswords heal and reduce damage). Moreover, Yelan is much better in AoE situations with her special CA and E allowing her to tag mobs of enemies.
If you're not using Bennett, a C0 Yelan can easily out damage a C6 Xingqiu. If you are using Bennett, then a C0 Yelan and C6 Xingqiu may provide similar sub-dps Q damage, but Yelan can still provide more damage overall because of her CA and E skills.
In terms of hydro application, C0 Yelan is good enough to compete with C6 Xingqiu. Yelan's Q does 3 per hit, whereas for C6 Xingqiu it is 2-3-5 (a bit more irregular), even with Xingqiu's orbiting rainswords. If you have C2 Yelan, her hydro application powercreeps Xingqiu. If you have C4 Yelan, she becomes bis support for Hu Tao teams (because of party HP buff).
And needless to say, C6 Yelan powercreeps Xingqiu in every possible way. But at that point, Yelan becomes a dps in her own right.
C1: extra charge is fine
C2: q fires 4th shot once in a while, increases hydro application, makes Yelan clearly better than XQ in all aspects
C4: hp buff for all party members
C6: enables more dps-focused Yelan, during her Q, each NA will do breakthrough CA damage
Artifacts: 4p emblem, 2p heart/2p tenacity, 2p heart/2p noblesse, even 4p wanderer's if you care about her CA. HP sands, Hydro goblet, crit circlet. Substats: crit, HP, ER.
Weapons: Aqua Simulacra is her clear bis. Other 5 star bows like TP, Skyward, Polar, Elegy are good. 4 star bows like Sac, Favonius, Stringless, Viridescent Hunt, Fading Twilight (2.7 event bow) are good. Even 3 star bows with crit are usable since Yelan scales with HP. In general looking for crit, ER and HP on the bow.
Anywhere you would use Xingqiu, you can replace Xingqiu with Yelan. Some notes: C4 Yelan's hp buff synergizes well with Hu Tao/Morax teams. Yelan even at C0 works perfectly fine with Yoimiya as Yoimiya does not care too much about hydro application, but cares more about Yelan's sub-dps and dmg bonus buff. With the new 3.0 update, hydro resonance now gives more hp to the team. So even a team like Hu Tao-Yelan-XQ-Morax can be played as Hu Tao, Yelan, Morax will all benefit from the hp buff.
In general in any team that wants hydro but does not need Bennett, Yelan can fit in as well. For example, in freeze teams and taser teams, Yelan works quite well. Not needing Bennett actually makes Yelan quite flexible for team building. In the abyss you can use Bennett on your other team, freeing up space.
But most importantly, when Xingqiu and Yelan are used off field neither of them benefit from Bennett anyways. Xingqiu's burst is dynamic and does not snapshot Bennett's buff (unlike say Xiangling's burst), so Xingqiu's burst when used off field does not benefit at all from Bennett. So in practice the HP scaling vs. ATK scaling does not matter as much as it seems.
Yelan can be played more as a dps than Xingqiu since Yelan does have the CA mechanic. This becomes more pronounced at C6.
Yelan scales with HP. To compare this dps to other users, we will set up a way to convert HP scaling into an equivalent ATK scaling value. Yelan has pretty high base HP, and with an HP sands, she can comfortably reach 30k HP. Meanwhile, most ATK scaling characters can say reach around 2k attack. With Bennett, ATK scaling characters can reach 3k attack. In other words, one can expect the HP to be around 10-15 times more than the total ATK. So to convert an HP scaling talent to an equivalent ATK scaling one, multiply the number by 10 (if using Bennett) to 15 (if not using Bennett).
There are two sides to HP scaling. On one hand, HP scaling talents are not affected by Bennett's ATK buff (one of the most broken buffs in the game). Moreover, there is currently no 'HP Bennett'. There is a 'DEF Bennett' (Gorou) who buffs characters' DEF. But there is no character who increases HP for all characters. This means HP characters usually need to rely on their pure HP scaling multipliers unless an HP Bennett releases in the future. Note there are passives/constellations that can buff hp (like Ayato C2 or Yelan C4), but this is still a far cry from an 'HP Bennett'. Yelan's C4 is probably the closest by buffing party members' HP (making her arguably the BiS support for Hu Tao/Morax teams), but how many people will be able to afford her C4?
On the other hand, HP scaling characters do not need to have Bennett on their team, which makes team building more flexible.
Based on the rule of multiplying by 10, Yelan's Q scaling is very similar to C6 Xingqiu's Q. So for C0 Yelan to do similar sub-dps to C6 Xingqiu means her dps is pretty good.
Assume lv10 Q. It will shoot 3 throws at most once per second. It lasts 15 seconds. Each throw has scaling 8.77% HP. At most there are 15*3=45 throws. Yelan also does an initial hit at 13.15% HP. The total hp scaling is $$13.15 + 45*8.77 = 407.8$$ This translates to about 4078% atk scaling (multiply by 10 as discussed above). Suppose Yelan uses 4p emblem with 200% ER (achievable with favonius bow or sacrificial as Yelan does not care much about atk). She gets 46.6+50=96.6% dmg bonus. The q cd is 18s. The q dps is $$x_q = 4078*1.966/18 = 445.4$$ This is more dps than c0 Xingqiu.
Moreover, she can give up to 50% dmg bonus (increases from 1 to 50 over time) with her passive to the on-field character. As Yelan is usually off field, we will not factor this into calculations here. But on average that is a 25% dmg bonus over time.
The e scaling (suppose no vaporize) at lv10 is 40.7% HP or about 407% atk scaling. It has a cd of 10s (shorter than xingqiu's E cd) and has greater aoe than xingqiu's E. The dps is $$407*1.466/10 = 59.67$$ This is without vaporize or the extra breakthrough barb (which has an extra 20.84% HP scaling and can also vape). So in all Yelan is a major upgrade to xingqiu. Xingqiu is now like a farmer that retired from work.
In her test run, she had 206.8% ER, 32556 hp, 105 em, 71.5% cr, 172.4% cd, with Aqua Simulacra and 4p Emblem. The build was pretty good.