Update on status:

I attempted a couple things: On the 'Modern' version of Firefox, I've updated Ublock to the latest version, and I changed "Enhanced Tracking Protection" from 'Custom' to 'Standard/Strict'.

This may or may not have fixed the problem, as it's mostly been loading now but I've also had a moment where it failed to load as previously. Not sure if this might at all be linked to if I have it set for 'Standard' or 'Strict'.

ESR version, however, still has the problem - I've attempted updating Ublock on ESR and changed the tracking protection to 'standard/strict'; however on ESR version of Firefox, YouTube still acts as if it doesn't exist.

Short version: I think I have YouTube working on 'Modern' Firefox (but I'm still concerned that may not last); however Youtube still does not load for me on ERS Firefox.

And sure enough, as soon as I post a message saying I think I have the problem fixed on the 'Modern' version YouTube immediately stops working for me again, though currently it's primarily acting as if there's just not an internet connection.

So problem not actually solved in any way I can consider reliable, unfortunately.

Rebooting my router appears to have fixed the problem for both computers.

Have absolutely no idea what caused the problem or why the problem seemed to have specifically targeted Youtube, but at least the problem is fixed, at least for now.