I have tried it on different days and at different times with different exit nodes. At the same time I am able to load new posts from relays, so I know not all traffic is being blocked/dropped.
When I spun up Tor Browser, and tried to go to getalby .com, I was given a captcha from cloudflare and the browser indicated that it was still loading even after the page was rendered (felt like a comet style pattern).
I realize there could be selective dropping of traffic from an exit node, and the main Alby website might not behave the same as the server that deals with the zaps and so forth, but it's the information I have.
What would be helpful is an error message saying the connection timed out (if that is what's happening). I have seen error messages when zaps get http status codes in the 4xx range, so I know those errors are handled reasonable well.
If you can make a test site that will let me input a nostr note ID and have it simulate what and app usinf NWC would do, I'd be happy to help test with the production network and sending real BTC around. A test site would allow you to see every step along the way and provide some level of confidence that the issue is not on your side.
I know it's hard when you don't control the code involved, and there's two men-in-the-middle (Tor, Cloudflare) before it gets to your servet, but if you try to use Amethyst and enable Tor, I suspect you will be able to reproduce the issue very quickly.