I understand the motivation for SIGHASH_NOINPUT - it would help with offchain payment channels. It was proposed already in the Lightning paper but Eltoo will effectively work just with something like that. But what exactly is the ANYPREVOUT BIP about? It seems like some extension to be used with taproot scripts. But I don't seem to get why you need a special public key type and chaperone signatures. Can anyone explain this part in plain english please?
There is not a real conflict between the proposals apart from the naming. The NOINPUT original proposal was we want to have this functionality and we’ll do it when the next version of SegWit comes along. The next version of SegWit is hopefully Taproot. The original way it was proposed meant that eltoo would’ve had to have been a CHECKMULTISIG script path rather than key aggregation Schnorr key path potentially. It is not technically any worse than what the original concept was by having to go through the script path. It is just the next progression now that we have some idea what the next version of SegWit should look like.