how to exclude user name from file paths in zsh terminal?

You control your prompt. But you do not control Blender, or any other app you run during your screen recording.

If you can find every place an app decides to display the full path, and there is a way to modify that code, then have fun.

I think it would be much easier to create a disposable user with a name that says what you want, then to find all the places some app or command or utility decided to display a full path with your user name in it.

what you want sounds like a Sisyphus task of constantly pushing a rock up hill, only to have roll back down, and start over again.

Blender is designed to output that full path sequence that you see as its absolute path, and there is nothing you can do in Zsh to alter that fact because it is program stdout content. The Blender developer would have to alter the application to output a tilde path string, and there is a single Apple Foundation NSString method to do that.

Can you not launch blender in the following manner from the Terminal:

open -a Blender

However, if you had an actual Zsh absolute file path in a variable:

x=/Users/myUsername/Library/Application\ Support/Blender/3.4/config/userpref.blend
print ${${x:a}//"${HOME}"/\~}
~/Library/Application\ Support/Blender/3.4/config/userpref.blend

Create another account for your screen recording.

Either delete the account later, or rename it, so that name no longer exists.

Change the name of your macOS user account and home folder - Apple Support