Can I get an extension on my Thai visa if I've overstayed beyond 60 days?

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.

Unfortunately, “good till the date on visa”, or 08 June, was the last date you could use the visa to enter Thailand. It has nothing to do with the length of your stay which is 60 days from entry.

It looks like you entered on 10 March, which means you are already on overstay. If that's the case you need to go to immigration immediately, get the extension if they will allow it, and pay the overstay fine