What is my legally allowed stay date in Thailand with a non-O-A visa and what options do I have for renewal?

NOW, let's look at the VISA itself.

That visa is a multi-entry OA and you can enter the country all you want on it right up until the 14th of Sept 2022. <- That's the last day you can enter and get stamped IN to the country on it

IF you got a new insurance policy that met the requirements before that date, exited and re-entered you would get stamped in until that policy runs out (up to a year).

There is no 'short term' buy you 3 more months to stay in thailand option on that visa that you can do IN country.

You have two choices

Just get a 3 month insurance policy, exit/re-enter the country on or before the 14th of Sept and get stamped in for the validity of the insurance.

OR

Just exit the country, go to a thai consulate nearby and BUY a single entry tourist visa, come in get 60 days, extend that by the 30 you can get at the immigration office for 1900baht and that would buy you the time until dec when you will leave.

Unless I'm mistaken the reason you weren't given a full year entry stamp is that you were stamped in only until your insurance expired (which is what I believe that hand written thai says under the stamp).

When does your health insurance run out?

At this time you can stay IN thailand until the 30th of Sept. <- it's the ENTRY STAMP that lets you stay here not the visa sticker