I’m not sure about Thunderbird specifically, but it works with any apps (like Kitty terminal or Slack client) on Plasma Wayland session for me. You’ve got no reaction at all, or is the task manager icon at least turning orange for attention?
This used to be a problem few plasma versions back as there wasn’t any standardized protocol for this, and then it got stabilized and implemented wayland.app/protocols/xdg-activation-v1
Is your default web browser set properly (check default programs in system settings, you might try and set it to something else then back)? And how about the following: