The biggest gotcha I can think of right off (which might not necessarily be a gotcha, but something to be aware of) is you'll need to work through your hostname resolution dealing with your public URLs. If your original environment is going to stay online during the migration, you might need to do some hostname resolution stuff until you're ready to make the cutover to your new environment. Of course, this all depends on how your current environment is configured.
This blog post does a great job of explaining what you need to do when using WebGISDR to restore to a new environment. https://www.esri.com/arcgis-blog/products/arcgis-enterprise/administration/migrate-to-a-new-machine-...
I'm not 100% sure on your last question. I want to say that you could use Enterprise/Cloud builder and then do a WebGISDR restore to it. I mean, using those builders shouldn't prevent you from doing a WebGISDR, so I'm thinking it would be fine, but I've also never been in that specific situation before.
Edit: To add on, the WebGISDR is at the software level, not server/cloud level. So I can't imagine there being any issues or gotchas when using WebGISDR to go from AWS to Azure. I'd imagine it would be more configuration related things at the server/cloud level and not the Esri level.
