At very least, BTCPay doesn't use Tor by default and in certain cases i expect to detect whether it's deanonymization attempt or network problem.
Tor is used by default for the WabiSabi coinjoin plugin in BTCPay Server.
There's 0 mention of keyword "tor" or "onion" on it's documentation though
https://docs.btcpayserver.org/Wabisabi/. Although i didn't watch included youtube video.