The caster is now only under the effect of true polymorph as magic jar has ended.
return to the caster's original body ends magic jar.
The original body of the caster of magic jar is true polymorhped while their soul is not in it due to magic jar. Their soul subsequently returns to their body ending magic jar or when magic jar ends.
...returning to your living body (and ending the spell)...
In either event, magic jar is no longer a consideration as it has ended.
The result is the same as the caster using True Polymorph on themself
The added hassle of the effects of magic jar are irrelevant as magic jar ends when the caster returns to their original body.
Could allow a caster to turn themselves into an object.
Normally, a caster can't do this to themselves as they can't maintain concentration after they've turned into a tea cup.
If the caster's original body was transformed into an object until dispelled via true polymorph, when magic jar ends, they'll either return to it and be trapped until true polymorph is dispelled or the caster dies.
If your body is more than 100 feet away from you or if your body is dead when you attempt to return to it, you die.
This depends on interpreting an object as your body, which is fair considering the edge cases true polymorph brings with it anyway.