This morning I've tried to pay again, and to my surprise the payment has gone through and my application is in processing.
Either the issue on payment processor side has been fixed (which is the most likely option), or me using the VPN, setting it to mask my IP as if I'm in the country where Thai embassy is located, helped.
My situation is a bit complex. We do have a Thai consulate in my country, but the Thai embassy (in another country) is handling visa applications.
Anyway, I hope my post helps someone in need.