MacOS – Updated Bash via Homebrew (from 5.0.17 to 5.0.18). Now I get Error message after starting Terminal

Your prompt is messed up, specifically PS1:

PS1=$[\033]0;37m]

that's missing a lot of escape characters (\e[) needed for the colors (and most useful parameters for a PS1). That's also why you get the 37m in the terminal window title. Try setting it to something different by running:

export PS1="\e[0;31m[\h:\W \u]\$\e[m "

and see if that works. It should give a red (thats \e[0;31m) prompt showing hostname (\h), current working directory (\W) and logged in user (\u) inside brackets [] and the bash exit status of the previous command (\$). Note that at the end the color is reset to the default of the session with \e[m .

If the above worked, you only have to find out from which configuration file your "bad" PS1 comes from: look for an "export PS1=" line in ~/.profile, ~/.bash_profile, ~/.bashrc, (as M K already suggested in his answer) and put in the above version.

There are a lot of answers around here with helpful colors codes and inputs for configuring the PS1, like this one for example.

.zshrc is a file run when you start an interactive zsh shell, found in your home directory. The error message says you have an export command which is written incorrectly on line 48. not valid in this context means you're trying to export something that's not a variable. It looks like you're trying to add stuff to your PATH, but are substituting the current path inside the zshrc file. Check that line in the file, there's probably a line along the lines of:

export $PATH=/some/directory/to/add/to/path/:$PATH

You just need to remove the first $ because it's substituting the current path there instead of assigning the PATH variable:

export PATH=/some/directory/to/add/to/path/:$PATH

See https://stackoverflow.com/questions/22394367/zsh-error-export54-not-valid-in-this-context