You CANNOT Derive the UTXO that Funded the Channel from the Invoice A Lightning invoice has no information about which channel the payment will go through nor which UTXO funded that channel. There's no public link between a Lightning invoice and the funding transaction. A node can have many channels funded from different UTXOs. Payments are routed through multiple nodes, the sender often doesn’t even know which node will receive the sats either, for example when using bolt12, or when using a lightning router service
Discussion
Okay, but lets say you know it's not bolt 12 or a router service, then you know the node id.
Can you get a list of channels from a node using the gossip network? I think yes. Especially because you can see it on an explorer. A random node example: https://1ml.com/node/039a3b0b2c86bb2b9fd5cf2c8ba52672b7fbd4b09de0031b9b7f5d76391f498f89
From that, you can see a bunch of channels and their outpoints. Those are the utxos.
Okay, so maybe you don't know WHICH one is the one you paid, but you know ALL of them partially belong to the recipient.
Bolt 12 is not so common yet, and I don't think many people think to use proxies.
Oh, I guess your best option is to have a private channel for sure.