bumi on Nostr: Actually there have been some experiments by Alby on this: ...

Actually there have been some experiments by Alby on this: https://github.com/getAlby/lite/

Alby Hub uses by default the Alby Relay but everything is e2e encrypted because of nostr.
It also uses the Alby esplora which just provides blockchain data.

If you don't want data to be shared you can set permissions (e.g. use an isolated connection to only create invoices).
You have all the options.