So what are the options for receving lightning that satisfy all of the following: self-custodial, private (doesn't doxx my node ID), always-on and uses invoices that are easily payable from common wallets.
Discussion
I use phoenix with fulcrum over tor.
Send postmix utxo and they open a channel for you. There is a 1% fee and they do a swap you trust them on.
Dump wallet when you are done and start over.
And people can pay invoices to you while your app is closed / offline? How does that work?
Yes, not exactly sure the technicals but I'd imagine they explain it on their git.
You do periodically have to open the app and it'll remind you with a prompt.
Tbh use it more for spending.