I'm very interested in new ideas for decentralized trading, so I looked at
your Github description. I've also had some (very early) ideas for a Nostr-based DEX protocol, but for a specific use case on a specific altcoin.
But already at the start I stumbled upon something I didn't like that much:
Every user has their Bank API and their Wallet connected to their open-source program.
I'm maybe a bit conservative regarding this, but I think with the scamming history on DEXes like Bisq in mind, a direct connection to a bank API may not be really a good idea - if hackers find any way to exploit that, they will. I think a human user should be the one to take the final decision about a transfer.
The part of the "sell request" is ok, I think that would be commonplace for all protocols based on decentralized/P2P chat/messaging networks.
B sends their bank information (suggestion: bank information = IBAN or IBAN + Name) to S
Here you should take an inspiration from Bisq: the account information on the "exchange network" should include a hash of the bank account information. So if you see a participant with an old account, then you can be sure that they operate with the same bank account for a long time. That's to avoid trading with parties using stolen bank accounts (they should never be able to operate for more than a month with the same bank account).
It seems the basic idea for your protocol though is the division of the bought/sold amount into many small parts, so in the case of one of the participants being unresponsive, neither party loses much money - and on the Bitcoin side you use LN to be able to send microtransactions without having too much fees. In general the idea to use LN with that in mind is quite good.
But there's a problem: Many banks suspect if they see many small transactions in the accounts of their customers. Maybe instead of bank accounts, digital wallet services which are commonly used for microtransactions could be used (however, only in some countries these have an unified bank account scheme, like the CVU in Argentina).
Maybe one could combine your idea of a LN-based protocol with an existing protocol like Bisq, to have a new payment option to "onboard" new users.