There are a few things like that, on the top of my head:

https://github.com/Overdr0ne/shelldon

http://www.howardism.org/Technical/Emacs/piper-presentation.html

I also recall seeing someone using fzf as a kind of interactive shell script engine, but I could not find that (reddit?) post

https://ambrevar.xyz/lisp-repl-shell/index.html

Unfortunately, I need to write Bash scripts only (for work). Since a shell is pretty REPL like, is there a workflow where I can "send" a few lines from a script.sh file to be evaluated in another window/buffer where shell is running?

Have you tried sh-script-mode? It has a function sh-execute-region for evaluating part of the script.