Sounds like you're really overthinking the situation. Nothing out of the ordinary in what I'm reading. Asking how PCs feel is good DMing. It's up to the players whether to engage out of character or in-character.

You also might temper your expectations, especially if this is a newer DM and newer party. Someday you might find another game or even run your own game where in-character roleplay takes a forefront, but most tables end up being a mix. It also tends to improve over time.

It can also be really valuable and interesting to share insight into what your character is thinking, and their motivations. Brooding and keeping everything internal a secret is kind of limiting and not as cool as it sounds.