Sent you some sats on your support page, unfortunately it didn't show it paid... but I get that it's possible :D
(I've seen some error "can’t establish a connection to the server at wss://nostrue.com/." but that may be irrelevant)
> How can you do that without access to the node who created the invoice and the payer app?
Through one of the various apis for it. I typically look for the allowsNostr flag, which is set to true in most lightning addresses, and then, when querying for an invoice, I request a zap receipt. The zap receipt, once posted, is how I tell if the invoice is paid or not.
> Is that possible?
Yes, I do it here, for example: https://supertestnet.org/support.html -- the "Lightning" option simply queries for an invoice from my lightning address and sends a request for a zap receipt as well, then starts listening for the zap receipt to be posted on nostr. Once it sees it, I show that the invoice has been paid.
> The node could tell you if the invoice is paid, but all you get is an invoice from an LN address
That's not all you get if you request a zap receipt; you also get reason to expect that once you've paid the invoice, a zap receipt will be posted on nostr and reference a pubkey or note of your choice, which you pass when making the request. And that zap receipt is one way to tell if/when the invoice got paid. Check out the zaps spec for more details.
Discussion
Ah, the pitfalls of designing nostr stuff that only uses one relay. The relay is down, of course, and showing an nginx error. 