Did you try Bitpay checkout payment option?
I have seen Bitpay payment on many websites which accept crypto as a payment option. Bitpay supports more than 150 different tokens/altcoins and USDT is one of them among some other major stablecoins.
Bitpay is a non custodial wallet so I think it will be decentralized without any third party app involvement.
And also 2% + 25¢* for crypto acceptance and KYC is required it seems but good part is settlement feaure for 38 currencies as fiat into bank accounts but their fee for crypto is too high since way better options there like nowpayments if u are after fiat settlement also
But it doesn't exactly offer non custodial service like Bitpay server with auto settlement into ur own wallet in USDT...