Say he’s not “impeached” but later convicted of a crime.
Either fraud, treason or something else. Could that then bar him from holding future elective office?
No. But NOT because he was impeached. Federal law requires that once someone has served as POTUS, they cannot run for any other elective office.
However, that does not preclude them from being APPOINTED to serve in a variety of unelected capacities. Again, Clinton and his liberal predecessor Carter provide us with examples.
In Clinton's case, he wanted to run for another elected office after his second term ended in 2000, but was prevented by federal law. In Carter's case, look how many times he has been appointed as a "special ambassador" to represent the U.S.' interests to a variety of oppressive dictators whom he loves and gets along with - to the disadvantage of America.