What was cool about the Gloria Sinica formations is that they applied to your whole army. So there'd be formations like "Flying Crane Wings" with the archers fanned out on the wings with the infantry up ahead in the center as the crane's head and the cav in reserve as the tail. Or there was one anti-horse archer formation where your troops set up a circle of wagons with the archers in the center, the infantry guarding the gaps between the wagons and the cavalry outside charging the enemy HAs. You could still use all the regular Warband orders, these just existed at a higher army level. That game actually had a surprisingly good "delegate commands" option too. My troops would do pretty well just fighting on their own without my input.
This is important, if you are going to lock formations behind perks.
These unlocks need to be
useful. I would imagine the majority of us always, on every battle, put infantry in shield wall formation and archers in loose and those are the only formation changes we make. And even on hardest difficulty, this is enough.
I would, instead, suggest that early perks give bonus to these common formations (line, shield wall, loose) where the main effect would be a bonus to active battles and the secondary a bonus to simulation battles.
Then later perks give big juicy bonus to the less used formations in unique situations, such as "35% damage reduction to units in circle formation when damaged by mounted archers". These perks would incentivise the player to adapt their playstyle and create distinct feelings to different encounters.
Peppered between these I would add perks for niche things such as world map benefits, retreat and disorganization (which honestly are all there and are the few good perks in my opinion). But also things like allowing the player to actively make their army look smaller to neighboring enemy parties with lower Tactics/Scout skills, as well as the opposite. Or the ability to let the player choose
where in the battle map they start in (closer or farther from enemy, already in the trees or in higher ground).
And this reinforces my point of Game Design. You want to enforce player
agency, make the player feel like they have control over the situations they are in and that you are giving them
new toys to play with. Perks that only add percentage bonus are FILLER PERKS. They are necessary to pad the perk tree but when most of them are like this then what is the point of perks when the Skill Level itself is all about percentage bonus itself?