Hanya 寒鸦 uses the 鸦 character also found in opium. Based on the 寒 and her clothing design, one would think she is cryo, but nope she is physical. That is actually ok since Eula is cryo but also a physical dps.
Her E applies a debuff to one enemy. Every 2 hits the enemy receives will recover 1 sp, up to two times. This can be useful for characters that can consume a ton of sp such as QQ or Lunae. It is also just useful overall.
Moreover, when an ally attacks a debuffed enemy the dmg dealt increases by 30% for 2 turns (so this is equivalent to a 30% dmg buff to the party, for st).
Her Q buffs one ally's atk (by 60%) and speed for 2 turns.
How do we translate the concept of SP into Genshin? SP is needed to use a skill. When one runs out of SP, one has to spend a turn or few to gain it back and use a skill again.
Perhaps one way is to think about skill cd. Gaining sp can be thought of as cd reduction or decreasing the time it takes to use a skill again. Consuming more sp may result in a longer cd (as with QQ or Lunae), similar to how Charlotte's hold E has longer cd than tap E (and same with other characters like kazuha). When Noctis uses his E (or Q) he can reduce the time for his CA (although this is a bit different it has a similar concept of time reduction). And then the extreme example is C6 Xiao where the E has no cd.
So given this, perhaps in Genshin, Hanya's E has the following effect: it debuffs the enemy, and every 2 hits it receives reduces the E cd of all party members by 50%.
Note in other thought experiments, we imagined that speed boosts could also act as cd reduction. If we want to distinguish spd boost from sp recovery, then we can say spd boosts could buff NA/CA atk spd (like Mika's E), whereas sp recovery is more similar to cd reduction (like Raiden's C6).
In Genshin, cd reduction tends to be underrated or even overlooked. Only when one sees things like C6 Xiao may one begin to appreciate how op cd reduction can be.
And yet again there are characters like Nahida, Focalors, Raiden, Yae, Albedo who have 100% uptime on E so that they do not really need cd reduction. Such characters can be seen as sp-positive in HSR as they do not need to spend sp each turn.