Actually, I'm a bit confused by @OP's story but I'm trying to understand as best I can.
I have only used P2P on Binance and always try to look for sellers who have the highest ratings and I can see some sellers have 100% completion on Binance.
The price difference may be slightly different from other sellers, but there might be a lot of difference in the ratings, so I'd rather pay a little more than get into trouble.

If you want to use P2P on DEX, make sure that the seller is a seller who has a high rating and a high level of success in transactions to avoid problems because they always maintain their reputation well.
We may still need an escrow agent to hold the money and complete the transaction so that both parties have no problems.
And it is right that if you do not receive anything, you do not have to release the funds and you can wait for their response to make the transactions.
And for the @OP case, he did the right thing by not releasing the coins until he received the money.