Topaz is a fire ST damage dealer. The way she works is almost similar to Albedo. Rather than being a 'hypercarry' or 'dps' (like Seele), Topaz is more of a subdps who can deal coordinated damage (via her trotter Numby) alongside your main dps. So rather than using her as the sole dps on the team, she can be paired with your dps and deal 'off-field' damage like Albedo.
So Topaz falls into a class of units that could be called 'sub-dps' in Genshin. Besides Albedo, some other subdps (via E) in Genshin include Nahida, Dehya, Yae, Fischl, even Kuki and Raiden (for hyperbloom). There are also subdps via Q such as Beidou, XQ, Yelan, but here Topaz is more of a subdps via E (skill).
Some of the best characters/supports in Genshin are subdps (e.g. Nahida). It is true they deal damage, but as they can be used 'off-field' they can also function as supports for things like elemental application, etc.
Indeed the way Topaz's kit works is almost like Nahida in the sense that: her E marks an enemy and does coordinated attack damage (Numby), and her Q buffs her coordinated attack's damage. Moreover, Topaz can have 100% uptime with her E, similar to Albedo and Nahida.
The difference between Nahida and Albedo is that Albedo appears to be more single target, whereas Nahida can mark multiple enemies. So here Topaz is a bit more similar to Albedo. However, it appears that Topaz can do more damage than Albedo as 1) Topaz scales with ATK (and can receive many ATK buffs), whereas Albedo scales with DEF (which is usually only buffed by Gorou), 2) Topaz's scalings appear higher and can be buffed by her own Q.
Topaz's pet trotter is named Numby. As the Star Rail universe appears to be outside the jurisdiction of Fontaine, perhaps we can rename Topaz's pet to 'Furina'.
Topaz can actually do a lot of damage per hit for free: e.g. around 30k per Numby hit, which is actually considered high among Genshin E subdps (Nahida, Yae, etc.) and given this is basically free damage with 100% uptime (not requiring much sp or energy).
In Star Rail, Numby is a summon (like Jing Yuan's LL) that starts with 80 speed. It will inflict a random enemy with a debt mark at the start of battle. Using E can also be used to inflict a single enemy with a debt mark. This mark increases the dmg it takes from follow-up attacks by up to around 50%, which is quite big. When a marked enemy takes damage from follow-up attacks, Numby's action is advanced forward by 50%. When it is Numby's turn, it will deal fire damage to the marked enemy (around 160% scaling).
Using Topaz's E on a marked enemy will be considered as a follow-up attack and will advance Numby's action. With one of Topaz's traces, her own basic atk will be considered as a follow-up attack. Other follow-up attacks (fua) include Jing Yuan's LL, Blade's passive, Himeko's chainsaw, Herta's passive, Kafka's gun, Svarog's passive, etc. So Topaz can synergize well with these units.
Moreover, the debt mark debuff can also increase the follow-up attacks of these other characters by 50%. In this way, Topaz can even act like a harmony support or buffer for other dps.
Also, Topaz is sp efficient (sp-positive, not needing to spend sp each turn). In fact, it seems the debt mark lasts forever, so for ST bosses it does not need to be refreshed. In other words, in some situations, Topaz may never need to use her E (making her one of the most sp efficient characters in the game). Of course, in practice Topaz benefits from using E on marked enemies to advance Numby's action more.
Based on her kit, she is more like a subdps like Nahida. So when building teams, one could use Asta or Tingyun. But rather than playing her as a hypercarry, it is more like she does additional damage alongside your main carry (so you would use Tingyun on your main carry rather than Topaz). Of course, there is nothing stopping people from playing Topaz as a hypercarry, using Tingyun to buff her damage, just like how there is nothing stopping Nahida from being played as an on-field hypercarry. But given how her kit works, she is more like a subdps (like Albedo, Yae) and can fit into many different teams to provide 'off-field damage' while not consuming much sp.
Topaz's Q buffs Numby's damage. It will double the scaling and increase the crit dmg by around 25%. Moreover, when allies' basic atk, E, Q hit the marked enemy, it will also advance Numby's action by 50%. This buffed state ends after Numby uses 2 attacks.
So Topaz is not exactly like Albedo. Albedo's E will do coordinated atk whenever allies damage the enemy in the field (with an icd of 2s). By contrast, Numby may not immediately deal a coordinated atk when allies damage the enemies. Its action needs to be advanced by follow-up attacks. And even within Q, other types of attacks can advance Numby's action.
As each attack can advance Numby by up to 50% (so two attacks up to 100%), this is almost like saying every 2 hits in Albedo's field will proc his solar isotoma damage. But that is almost true since Albedo's E procs once per 2s. Even Nahida and Yae have icd on their E as well.
The whole point is that it is not like each character's atk will proc Numby's coordinated atk. If Numby dealt damage every time a character hits a marked enemy, then Topaz would be the most broken unit in the game (30k per Numby hit, times 4 for each ally, gives 120k free damage per turn). Moreover, if Numby did aoe dmg rather than ST, there would basically be little need to pull other characters (30k to a single enemy, times 4-5 in aoe situations, giving up to 150k per hit, and if that procs every time an ally hits an enemy, that is times 4 per turn for 600k free damage per turn).
By the way, the above also shows how broken Nahida is given that she actually can nuke multiple enemies for free with E.
Anyways, Topaz actually turned out better than expected and is quite a good unit. Her kit is a good upgrade from Albedo's, and she can do good damage.
In Genshin, Topaz would be like a pyro Albedo/Nahida, an E subdps with 100% uptime. Note we do have Dehya as an E subdps (she gets near 100% uptime at C2).
Topaz's E creates a field (say 10m in radius like Albedo's E). Or you could make it like Raiden's E. Say the field lasts 30s (or forever), and the E has a 4s cd for 100% uptime. When enemies in the field take damage, Topaz will do a coordinated pyro hit (occurs once per 2s) scaling with her ATK (say 160% atk scaling).
We vouch for just a simple 2s limit and avoid having to define what a follow-up attack means in Genshin (one could say if enemies take damage from off-field abilities like Nahida E, Yae E, Albedo E then it will proc Topaz's E, but that seems a bit restrictive and overcomplicated compared to Star Rail, so we choose to go the simpler route). Besides, Topaz Q and passive allows Topaz own basic attacks and other allies' damage to proc Numby's damage.
Moreover, enemies within the field take up to 50% more damage. Actually, this may make her too broken (Mona Q buff is 60% universal dmg buff). We want to say take 50% more damage from follow-up attacks, but as mentioned above how do we define follow-up attacks in Genshin? For this, maybe we can say 50% more damage from off-field abilities (Nahida, Yae, Topaz, XQ/Yelan, Kuki, Mona E, etc) as well as Topaz's own E cast. We could also try 50% more damage to pyro attacks specifically. Whatever we choose above, the buff is actually pretty good.
Topaz's Q doubles her E damage (to say 320% atk scaling per hit) and buffs its crit dmg for say 15-20s (compare with Nahida Q buff). Moreover, it will increase the rate at which the E can proc. Rather than proccing every 2s, it will proc say every 1.5s.
And if you want to make her even more broken (like Nahida), you can say her E has no icd on pyro app, so that it can melt/vape every hit.
One of her passives can restore energy after using Q.
In Genshin, Topaz's best 4p set would be Golden Troupe. She could be played as a universal buffer with her E, in melt/vape teams, rational/national, fit into most teams (even Xiao, Itto) as a subdps, and even work as an off-field burgeon/curry driver.
Given this info, we can actually compute her mv. Say she has pyro goblet (46.6%), 4p golden (70% off field), and the 50% dmg buff from her field for a crazy total of 166.6% dmg bonus (Xiao levels of dmg bonus). Moreover, suppose we have her burst on 100% uptime so she does 320% atk scaling every 1.5s. Moreover, suppose we can melt each hit (say by using an on-field cryo enabler like Wrio, Ayaka, Chongyun field). The mv is $$x = 320*2*2.666/1.5 \approx 1137.5$$ which is insane at C0. And we are ignoring the crit dmg buff. So if we care about 'balancing', then perhaps some of the numbers above can be tweaked.
But this napkin calc just shows that if we transfer Topaz's kit as-is to Genshin, she would be a very good damage dealer.