A statechain UTXO is co-owned by the statechain operator and the last recipient in a multisig. Multisig inputs do not participate in the secret derivation.
I do not understand what you mean by secret derivation here but swaps are possible using statechains. It is described with an example in this blog post: https://uncensoredtech.substack.com/p/octojoin
Submarine swaps refer to a multi-hop lightning payment whose last hop is executed as an on-chain payment to the recipient. Submarine swaps are easily identifiable via an on-chain HTLC construction and also include a multisig construction.
This is a swap tx using boltz and looks normal to me: https://mempool.space/testnet/tx/e72f8323de0fa8eb9540041a787d4b89694040fd0a674701877f0a352b8f3685
A coinswap is a payment received to the recipient whose inputs were not controlled by the sender.
https://github.com/citadel-tech/coinswap can be used to swap UTXOs which will be part of octojoin transactions along with normal inputs.
If an observer simply categorizes the inputs and analyses their pedigree under the corresponding context, it seems likely that a transaction would be sufficiently recognizable as an Octojoin and given the small number of Statechain and Submarine Swap providers, potentially even identifiable via information requests to such service providers.
Octojoin transactions will always look normal on-chain. Leak during swaps is out of context for this BIP still added as attack vectors.
Could you please expand the motivation section by elaborating your arguments why participation in this scheme is expected to lead to a privacy improvement?
Done