Why might pasting an URL link into iCloud from a PC make that link inactive on iOS in notes?
I made a short clip of how the web app works when typing.

My guess is the paste event isn't triggering the URL detection and I can replicate the behavior you describe on Safari by pasting in and matching the style - even when I cut the URL that was detected by my typing.

All I need to to is add a space after the paste event and the URL gets encoded properly and turns blue as shown in this short video...

So, you need to type a space to get the paste to be processed.