The rustc and cargo updates are almost ready, so I expect the firefox update should be unblocked today. It will still require a bit of time to build and validate, but if everything goes well before the end of the week it will be available to all users on all supported releases.
In the meantime, the firefox snap is a good alternative.
The canonical repository is on GitHub, and it is mirrorred on Launchpad where the snaps are built.
This time, for Firefox 106, as far as I know, the Rust toolchain is not responsible, but Firefox 106 has been since 13 days (or 6 days - 106.0.2) not published, although built a long time ago. What is the problem? There are some important JavaScript security fixes included…