Couple of amateur ideas. If there is any room to maneuver the nut, or
rotate it, take a piece of stiff wire and try to fish it backwards into
the tank. It got in there somehow, so my guess is that will work.
If you cannot maneuver the nut, you somehow have to reverse the water
flow back into the tank. Try a pump or siphon (if you have the nerve)
to suck the water from the bowl back into the tank. This would work
even better if you tape off any other jet holes at the top of the rim.
If you can accomplish this, my guess is that wire nut will be sucked
right back into the tank.
One last suggestion, try to figure out someway to epoxy or otherwise
attach the nut inside so its presence doesn't affect water flow. just
put a dab of epoxy on the end of a q-tip and smear it on the far side
of the jet hole, then press the wire nut to it. Although this isn't the
best solution, it will at least give you some temporary satisfaction
and the toilet will function.
Let me know if any of these sound feasible. Good luck

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