I think we should focus on a KISS solution: keep it short and simple 
@jakfrost : Am I right that your current goal is to create a working terminal on the damaged system to then do further investigation on the terminal? Therefore, a simpler implementation of the chroot approach above? I do not know much about the rescue option because I have not yet needed it, but if the rescue provides only the same outcome as the chroot approach (which is a terminal that uses the damaged system as root), I think the easiest and fastest way is to use any live system to backup the data using the GUI (the btrfs drive seems to be ok), and then simply install a new Fedora. Even if the logs contain sufficient indication, it is likely that complexity even increases in subsequent steps.
@perryt :
→ Do you have backups of the data that is stored on the damaged Fedora? You do not need backups of the operating system itself. I mean only backups of your own data (private data, business data, documents, pictures, videos, and so on).
→ Would it be a problem to delete your Fedora and install a new Fedora? If this approach is ok for you:
You can do this with a live system, which you can create with the media writer (for this, use the mediawriter, and create a Fedora Workstation 36 (not Server!):
If you have not backups of all your data, start the live system, click on Activities on the top left and open files. Then the file manager opens. On the left, click on Other locations. Then, check out the drives on this computer : One of them is your old Fedora, which contains the following folders: home, root, timeshift.
Search in these three folders for the data you want to backup. Use an additional USB storage and backup this data (it has to be an USB storage other than the one with the live system; maybe you can borrow a USB storage for a day if you have no second one?). You can do the backup activities in the file manager. Check out on another system if the data is backed up on the USB storage! Now you have a backup:
If you have backups of all your data, start the live system, click on Activities on the top left and open install to hard drive. In installation destination, use automatic, done and then reclaim space. Then, delete all and then reclaim space. This will delete all remaining data on this system! Of course, you can also do this manually instead of automatic.
If all your private files are stored on the home partition, you can re-use this partition without formatting it (installation destination → custom → mount+format boot, mount+format root, only mount home without format). In this case, you can create a new Fedora installation without deleting your private files. However, in this situation, I suggest to not try anything without a backup!
Hope this helps.