I started with Leon, and I can confirm that the second thing you mentioned happens in the Leon A campaign as well. Another thing I noticed is that Leon always saves Claire at the Gas Station regardless of who arrives and discovers the scene first. Either Leon will shoot the Zombie sneaking up on Claire as she enters and he exits the Gas Station (Leon A), or he’ll shoot the zombie as she exits and he enters the Gas Station (Claire A).
Ada and Claire are both complete badasses but there are just these little moments that undercut it for… no real reason? It feels bad.
EDIT: I also want to add: the best way to go imo might actually be Claire>Leon because in the B playthroughs each character gets a special handgun that takes a new kind of ammo, and most, if not all, 9mm pistol ammo is replaced by the new kind of bullets. I am not vibing with Claire’s new pistol at all and prefer her starting gun, but theres literally no ammo for it. it sucks!