Savings bank accounts have limitations. For big transactions you can have a business account . Based on the location of the bank (country) and the terms we'll be able to see different volumes to be transacted. The process of p2p trading will be the same with majority of the trading service providers. You find a trader, open the trade, make the transaction and the volume of cryptocurrency for the amount transacted will be sent to the respective account's wallet.
I think this important about some people active in P2P trading, some Bank account have limited for withdrawing or sending fund to other Bank account and need upgrade become business Bank account if want to make huge transaction in P2P. I think this rule for buyer only because he needs sent fund to seller trough P2P could be in Binance exchange, OKX, Kucoin and many exchange have support with P2P nowadays.
Talking about transaction process in P2P trading based on how trusted buyer or seller there, some people looking for seller with lower price for stable coins but have bad impact with low respond and some time we have contact support for releasing our transaction and some time have cases for refunding fund have been sent.