Instant exchange platform such as ChangeNOW or SimpleSwap act as service intermediaries. They have their own liquidity pool and central reserve. When we swap through them, we send them fund to an address and they send us fund from their address. It is P2B or Peer to Contract model.
It is not Peer to Peer by any mean. Because rate and condition of third party platform have to be followed.
Ofcourse, a better decentralized exchange should be done within a shared opensource platform that a peer can't unilaterally control, and that allows for running of nodes with smart-escrow/contract where exchanging funds are temporary held and later released to exchanging peers once term of contract is fulfilled or the right amount of funds from both peers are received by the smart contract.
Yes, to be true P2P transaction, this must be the case.
Funds will always be in on chain wallet controlled by your private key before and after transaction.
Open source platform like Bisq, Hodl Hodl or RoboSats are closest examples of true decentralized P2P today.