I have tried the solutions suggested here but none worked.
The issue is easily reproducible, just run :ter source ~/.zshrc
No special requirements for .zsrch and the .vimrc files, they can be empty (but I tried to add set shell=zsh and set shell=zsh\ -i in the .vimrc as suggested in the link I posted).
However, if you run :ter, wait for the terminal to open, and then run source ~/.zshrc from the terminal buffer everything works fine.
I am running on Mac OS X Ventura and I tried with both the shipped Vim 9.0 and MacVim.