What's the best way to verify that you...

1. Made a bitcoin payment to an address

2. Paid lightning invoice with your node

3. Paid a lightning invoice with a custodial lightning wallet

4. Paid a lightning invoice with an eCash (Cashu, eNuts, Fedimint, etc) based wallet

These are progressively harder, if at all possible

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Discussion

1 is easy, sign a message against a private key. It's what CW needs to do for the genesis block to prove he is Satoshi. The same mechanism applies to any key ownership questions.

No clue on 2 & 3.