Personally my recommendation in situations like these is to look for another avenue. In this case, it looks like Betterbird is available via Flatpak. You can set up Flatpak via your NixOS configuration then use it normally.
If you want to declaratively install Flatpak applications, there is nix-flatpak. See the project page and discussion.
Of course, this has a number of trade-offs and might not be the right choice for you. If you would prefer lifting the derivation into your configuration instead, we can probably help you figure that out. However, if it’s much like the Firefox build process, without the benefit of Hydra caching, this will probably not be a great experience.