You can simply escape any % characters that you need in your url (or anywhere else in PAD) by adding another % character in front of it. This will ensure that PAD doesn't think you're trying to use a variable, and it will still only send one % when launching the browser. I'd recommend a quick 'find and replace' on your value where you find % and replace it with %%.
Here's an example:
Original URL:
https://www.google.com/search?q=power+automate+%25+character
Escaped URL to enter into Power Automate Desktop:
https://www.google.com/search?q=power+automate+%%25+character
Double % when entering the value in Dialog:

Correct URL Launching in Browser:

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Cheers,
Matt