How do break bars change the game? (And when?)

Break bars are very annoying. It's not just about wasted damage; it's also about the buffs that the enemy gains or debuffs your team get once one of their health bars is broken. Granted, this doesn't happen all the time, and sometimes the enemy may even get some debuffs once one of their HP bars depletes, but those cases are rare.

Take a look at Verse 16 of the SIN chapter for example: https://fategrandorder.fandom.com/wiki/Main_Quest:_S_I_N#Verse_16

I had one heck of a tough time because of Heretical Doctrine・Vicissitude​ of Flowers.

My choice of CEs and Servants doesn't really change, as I still bring Merlin along for Boss Fights (His NP is a huge lifesaver).

As for when, it will be during the Shinjuku chapter release a few months from now.

I don't think it changes playstyle much other than making AOE servants more attractive than they used to be. Big NP nukers can still work, it's just the ones that have trouble consistently charging their NP that have a problem, and that's still easily solved with supports.

It basically makes the game goes " Oh you want to nuke this round in one go? Too bad, now they have this monstrous buff that you have to either stall or have another way to deal with."
It's annoying at times, but it doesn't change much beside making spammable NP servant and/or tanky servant with decent damage becoming better than nuker servant.