Just being an old ea81 I’d go through a few items, maybe one at a time and test after each.
There’s a few changes as the EA81 goes on but yours may have the black plastic flying saucer looking thing which is upstream from the carb. One recorded event was that plastic breaking apart and minute bits and even chuncks getting into the carb.
Also the flaps on the air suction valve. Four Phillips screws on the metal box with hard metal tubing. Check those flaps for serious degradation at the lower edge kind of like an old carburetor slide if you’ve ever seen a lawnmower or motorcycle carb.
Heat causes expansion so then can create leaks. Spray some wd40 or carb cleaner around the base of the carb as it’s warmed up and running and see if the idle levels out.
Several folks here still active with EA 81s so you’ll get more advice soon.