Stop sending User-Agent. Replace it with nothing. Not client hints. Nothing. If sites start rejecting Firefox clients because of that, then instead change it to send exactly the same User-Agent (and other software identification) that Chrome sends, and commit to exactly faking Chrome's signals in the future. The UA header never had any business existing to begin with. Servers guessing client capabilities from the sof…
We live in the 21st century and have proper APIs to detect features now, we should not be relying on parsing this user-agent string which is 90% legacy-garbage anyways.
I mean, sites blocking compatible browsers is such a common problem that not only do user-agent switcher extensions exist, they're also some of the most popular extensions out there!