Separate from Ravi's authoritative answer to your specific question, Al, I would note that your inability to update in the admin (and the failure to connect) may be very simply resolved by updating the jvm you have cf pointing to. That's not quite the paradox you assert, as updating the jvm is NOT done by updating CF, as you may know. 🙂
To be clear, the jvm that cf COMES WITH will either be 11.0.1 for the ORIGINAL cf2021 installer (from Nov 2020), or 11.0.11 for the "refreshed" installer offered in Sep 2021. Those are both old. Sadly, if you download the installer EVEN TODAY, it will be one OR the OTHER depending on how you obtain it from Adobe. (That really is tragic, and leads folks to be in the very pickle you describe.)
So first, you can easily see what jvm version cf is using via the cf Admin settings summary page (among other ways). What is yours?
And second, you can easily update the jvm. I have both a blog post and a presentation covering that (and this reason it's needed). I don't sense those are resources you've necessarily already considered; however, I can say they're not specifically "written for Windows", though they may well show some solution that is. I try to be as OS-agnostic as possible. 🙂
Finally, as for the rather convoluted new approach (of extracting a zip and using the command line cfpm tool), newly discussed in the update technotes since update 2 of CF2021, I will just say that the "old way" (introduced in cf10, of using the java -jar command to point to the downloaded jar) still works, even with the latest cf2021 updates. I have covered that approach also in past posts and another talk. Granted, that's from 2019.
And Adobe must have their reasons to promote this newer manual approach, but I've not found it to be NECESSARY over the old manual approach--when updating cf and ALL modules in cf2021. Ravi or anyone else, if you may care to share more, please do.
But Al, my point is that updating cf (manually or otherwise) may not necessarily BE your best first step, especially if you would see the other security benefits of updating Java anyway (see my posts or talk ON WHAT updates are appropriate--currently 11.0.16.1, as of Sep 2022).
But at least you have multiple options and resources to consider now. Let us know how you go, whichever you use.