Some shops will plug run flats, some won't. It also depends where the puncture is. If it is too close to the sidewall, you can't patch it up. I think for your situation, if the puncture isn't close to the sidewall, it is safe to patch it, since it was never driven completely flat. The only concern of patching/plugging run flats is damaged inner walls due to being driven completely flat.
If you decide to replace the tires, check the other rear tire and see if there is still enough tread left. The only thing people would say when you replace one side is that you'll notice a pull. I replaced my left rear tire with a used tire (about 8/32 left) when my right tire only had about 4/32 - 5/32 and didn't notice any sort of pull.
Good luck!
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