If you entered on the 10th of March 2022, counting 60 days from that time your visa should be until the 8th of May. Since you didn't extend your visa on or before the 8th of May, technically you are overstaying from the 9th of May until today (12 days). That's 500 THB per day. If you are going there this Monday, that's an additional 3 days. You can pay the overstay fees and pay for your extension of 1,900 THB too.
The process at the moment is for you to enter Thailand with a Tourist Visa or Visa Exemption and either can be converted to an Education Visa in Thailand without you leaving again. And yes, paperwork has to start immediately upon your arrival.