It’s good to feel stuck in analysis mode and feel like there’s no golden build for a particular hero. This is healthy and leads to learning the ins and outs of the hero in question (especially about unit matchups). It may also prevent you from making decisions you might regret later. The long game is far more important than the short game in FEH, generally speaking. I’d speak more to that notion but it’s clear you like Hana as a unit and you want to make her as useful as possible.
Vantage build only really works if she can clean up weakened melee opponents and Armors she can slay. She’ll need as much Savage Blow support from allies as possible to weaken them. She pretty much has to run Distant Counter and thus loses out on the valuable A skill slot in doing so, so she can’t pad her stats any further, plus she’ll still crumple to tankier opponents who can soak a single Vantage attack. She also benefits immensely from PP-oriented skills rather than EP-oriented skills, so an EP build is definitely weaker on her. I don’t suggest Vantage, I only suggested it because you seemed set on using her as more than an in-and-out assassin.
I agree with @anon80299318 that FB4 is a really niche skill and probably shouldn’t be run most of the time, especially when you can run the infinitely cheaper FB3 seal instead. There are also heavy risks to using Galeforce on a unit that wants to absolutely murder its target; if she deals too much damage then she can’t proc Galeforce in a single round of combat. Galeforce also requires that she take a hit from an opponent, since she doesn’t get a Slaying effect in her weapon.
My suggestion is to make her stand out doing what she does best as much as possible. Focus on what she can do that no other unit in Heroes can do as well (or what she can do much cheaper, since she’s in the common summon pool and not 5* locked). To me, this is her power as a Player Phase oriented assassin swordie + armor killer. Only Phina can really compete with her in this category (I’d say Phina is just outright better than Hana, but again, 5* locked so an expensive option for many). Hana can stand out at this role pretty handily without a high-investment build, but there are obviously higher investment options available. I came up with this general purpose build using mostly easy-to-acquire skills for inheritance:
I put Glimmer as her offensive special because 60 base Attack is pretty high, although it won’t scale as well against extremely high-Defense enemies. You have Ruptured Sky already, which I’d say is a bit less consistent but can be great against high-Attack enemies, although Desperation will largely take care of this issue allowing her to avoid damage from those enemies. She can also run Moonbow if you need to puncture enemy Defense better. It depends on which targets you find her up against more often. Without Desperation, I do not recommend having her attack most full-health dragons even if Ruptured Sky is good against them. She will die.
Fury + Desperation works very well on her, she can even prepare Desperation before combat if she uses Reciprocal Aid twice (which supports the team, since she can heal up allies if idle) before attacking or once if she gets hit by an enemy Savage Blow attack. She can also use it once and then delete an enemy she easily overwhelms or OHKOs, take 6 damage from Fury 3 in the process, and be in Desperation range. Or just engage in combat twice in a row taking no damage, take 12 recoil from Fury 3, and be in Desperation range. Etc, etc. Unfortunately she can’t use Reciprocal Aid just once then be primed, because 36 / 46 HP = 78% HP, just shy of Desperation range. And since she’s an offense-oriented unit, her teammates will more likely be the ones using support skills on her to get her out of enemy range after combat. You could also just go with Reposition or Drag Back if you want her to do the same for her allies.
The build focuses on her PP offenses. SS2 in her weapon means she only gets those boosts during Player Phase engages and those stat boosts are in-combat, not out of combat, so they cannot be taken from her via Panic status, enemy Lull/Dull skills, etc. Hitting 64 Attack during combat before factoring in visible buffs is pretty good–it’s easy to give her extra Atk with either an Atk Wave skill in her C slot or via ally buff support (L!Azura is ideal to grant spectrum Tactic buffs) but without visible buffs, she’s basically Panic-immune.
Fury 3 is cheap (4* Hinata) and effective, gives her some much-needed bulk + most of the stat boosts Life and Death would give her but with none of the statistical drawbacks, so she can soak hits better. Fury also gives her recoil damage to help trigger Desperation easily in future engages, and won’t kill her since it’s out-of-combat damage.
C skill is very flexible. I put Rouse Spd/Def 3 because it’s rather cheap (promote 4* Ferdinand) and gives her much-needed physical bulk and Speed for Desperation in many situations, but it’s neutralized or even works against her with the Panic effect, Lull/Dull skills, etc and those are very common in PVP modes so it requires smart play to work around. You can also run a more team-supportive skill like an Atk Wave or Spd Wave skill, or a more expensive fodder skill if you wish. A Smoke skill also works if you want her to entirely support her allies who will swoop in and cover her butt after she eliminates a target, or with dancer support so she can take advantage of it as well.
I put Heavy Blade 3 seal due to how hard it is to compete with Speed creep lately, although Flashing Blade 3 seal is almost always better against beefy tanks/armors. Both of them work perfectly with 2-turn specials. I am not entirely sure about HB3 myself without testing it, as her 60 base Attack, which (without a boon) matches +1 +Atk Edelgard–and in combat becomes 64–before visible buffs and ally Drive skills support is pretty hefty, but it’s possible she may run into extremely high-Attack targets she cannot proc HB3 against (or an ally might be running it), in which case FB3 works wonders. You can tune her C skill or even run Life and Death 3 (4* Sothe) as an A skill if you need the extra Speed to trigger FB3, but she will be very squishy and prone to getting OHKOd so I don’t recommend this. If you just want her to outright murder opponents without special proc reliance, Swift Sparrow 2 seal can beef up her engagement offenses even more.
Again, this is all theoretical–haven’t run any combat simulations with her. I highly recommend doing so to test theoretical builds against her top matchups. This was fun to work through, I’d thought myself about building up Hana so actually exploring her options was fun.
EDIT: I did run one combat simulation to see how she holds up with the build I gave her in a mostly unfavorable matchup: initiating on a +10 +Atk base kit Brave Hector. Assuming no other buffs except Rouse Spd/Def (on her) are active and she starts the battle at full health, she ties him for Attack–this means she loses Desperation and Heavy Blade 3–so the fight is more even and a better example of how powerful she is. She barely survives initiating on him with 2 HP and kills him after his first counterattack:
If she has taken 12 or more damage, she easily beats him taking no in-combat damage and still without activating Heavy Blade. With Life and Death 3 at full health, she would outright die on his counterattack.