One of the advantages I've heard about Taproot is that all transactions will appear identical to a blockchain observer. This would of course also be true for lightning channel open/close transactions as well which would be a great privacy benefit for lightning users.
For what I understand of the proposed ANYPREVOUT upgrade, it will build on top of Taproot but will need to use a different length pubkey. Would it be possible for an observer to scan the blockchain for this pubkey length in order to determine which transactions are using ANYPREVOUT, and are therefore likely to be lightning related? Or is it possible to somehow hide this inside Taproot in such a way that privacy can still be maintained?