M-x shell does run bash (or whatever is your user’s shell)

M-x eshell is a shell implemented completely in Emacs Lisp and integrates with Emacs really nicely

Did you try swapping or replacing capslock w/ ctrl? Something like this...

    setxkbmap -option ctrl:nocaps
    xmodmap -e "keycode 107 = Control_R"

I would occasionally experience some pinky pain until I did this. Losing capslock is mostly inconsequential (you can always use upcase-region).

This is a useful guide to the different shells in emacs:

https://www.masteringemacs.org/article/running-shells-in-ema...

(the whole site has lots of information about emacs)