macOS Big Sur Terminal hangs and no prompt appear
Typically this is a dot file causing the shell to hang.

Make a new account and log out of the old one - log in to the new and open the shell. If it hangs, too - you have system level configuration files to blame in most cases. Reinstall the OS if you can’t Seuss that out.
If that works fine, then su - hanguser to confirm it’s that one account.
You can run the shell without the rc dot files as well.

Also, before you try anything shut down the OS and validate it happens after a restart, basically try to avoid needing to go through this laundry list of potential issues:

Terminal login hangs