Solved: Turns out it was an addon.
Description of the issue:
YouTube will load videos longer than usual by presenting a loading indicator. This seems to be related to YTs recent “crackdown” on adblockers since this problem does not present itself on unmonetized videos. Note: YT may play ads even on unmonetized videos, so testing maybe iffy at times.
I’ve tested this on a “Carbot” video (which is a popular channel with typical ad-enabled content) as well as my own channel (which lacks any monetization options as I’m not a typical “YT content creator”). My videos would load instantly, while Carbot’s would display the loading indicator for a while after opening video.
Exact URL of the website in question:
I’d rather not paste any direct links to any specific videos, but generally it seems any monetized video will have this effect.
Did the issue present with default Shields settings? (yes/no)
Yes.
Does the site function as expected when Shields are turned off?
Yes, but… While a video will start playing immediately with shields off, this video will most likely be an ad if the video in question is monetized. An unmonetized video will work the same with Shield as well as without.
Is there a specific Shields configuration that causes the site to break? If so, tell us that configuration. (yes/no):
No
Does the site work as expected when using Chrome?
Yes… assuming one wants to watch YT ads. 
(See answer about disabled Shields)
Brave version (check About Brave):
138.0.7204.97 (i.e. latest beta)