Although it's not an ideal solution you can also use "Legacy Software" but its database will contain applications that you may have already deleted. It won't find 32-bit processes either, but it's better than nothing.
Might anyone have any idea of why the System Information plug-in does not respond quickly enough to allow display of applications?
I'm afraid I don't know, and you already tried "Safe Mode" which would have been my suggestion. I do know it can happen from time to time though. I doubt reinstalling macOS will help.
Edit: You can use mdfind which will leverage Spotlight to find 32-bit dependent architectures. Or, simply use the Finder's Search feature (which does the same thing).
I've read your suggestion about Go64 on your other posts but I'm always hesitant to add more software to a machine that may have issues.
Although I wholeheartedly agree with concerns regarding adding unnecessary software to a Mac, Go64 occupies very little space, doesn't require an installation procedure, doesn't alter your Mac, and you can just drag it to the Trash when you're finished with it.
If you have reason to be concerned about "issues" please describe those concerns. I'm just wondering if there's more to your question.