Even I’m facing a similar issue.
Two of my payment methods – UPI & Bank Transfer are not working and neither they throw any error.
Payment Gateway – Both Razorpay & Open are not working too, routing to 404
So in short, I’m not able to sell anything from my website and customers are calling us/logging support tickets with us back to back.
I strongly believe something is wrong with WooCommerce 4.4.1