I can report that the COM Registration Tool in NVDA 2021.2rc1 was able to solve a problem that the version of the tool in 2021.1 was unable to fix. The symptoms were as follows.
I don’t know what change caused these issues. I may have uninstalled something at some point that deleted registry entries which it shouldn’t have changed.
Fortunately, all appears to be in order after having run COM Registration in 2021.2rc1.
The system is Windows 10 21h1 (64-bit), build 19043.1202. All of the browsers concerned are up to date.
I’m noting this here in case it helps someone who encounters similar issues.