Does the future SIGHASH_ANYPREVOUT capability hurt the privacy of Taproot lightning channels? 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?
The foundation of a channel is a multisig output which can't be distinguished from other outputs when using musig and taproot.
The mutual channel close is just a regular tx spending this output so I'd say it'll be hard to detect this as a lightning Chanel without other data (similar as with current channels)
However the unilateral close is different and leaves a footprint of the channel state. I think the update transaction that is used to kick of the settlement tx might have the detectable structure that you have been referring to. (I'd actually like to ask you for your source)