I kinda went through this recently. I had been experimenting with both tilix and alacrity. I'm going by memory now on the phone, so bear with me. I ended up deleting the apt extension thas is actually the functionality behind the default "open in terminal". You kan provably find it with a "dpkg -l nautilus | grep terminal".

Then I installed some nautilus python package (I don't remember the exact name), which seems to be integrated. I also installed through there some project that was supposed to add any terminal. At the end it showed multiple entries for alacrity and tilix. So I uninstalled the package. And suddenly then I had just the entries for the terminals I used.

That said... It's not great that nautilus doesn't respect x-terminal-emulator. That is exactly what it is for.