"right" click the app and select "Open" creates the same exception without the need to open settings. There's also an equivalent terminal command for the exception I can't remember.
If either of those aren't satisfying, you can always drop the check entirely which I can't personally recommend.
I don't think you can? Unless I am missing something?
You can add Terminal to "developer tools" so you can launch stuff from the shell without Gatekeeper interfering, but is there really a way to disable the gatekeeper warning for downloaded apps altogether?
I've just tried that, and I still get the gatekeeper warning, so it doesn't seem to work anymore on macOS Ventura.
Executing the command does make the "Anywhere" option show up in System Settings, but from testing it doesn't seem that this option makes a difference.
If either of those aren't satisfying, you can always drop the check entirely which I can't personally recommend.