I’ve never heard that the impeachment hurt Gore. In fact, what I always hear is that Gore running away from Clinton backfired.
And why did he run away from Clinton to begin with? Rhymes with lin-deechment.
The 2000 election was close enough that you could make the case for a hundred different things making the difference between a Gore win and a Gore loss. Nonetheless, I think the narrative about impeachment costing Gore a win lacks strong supporting evidence. It seemed to emerge largely because people wanted to make the point that impeaching Trump would actually benefit Democrats politically (and they seem to have been wrong there, given that Trump's approvals are currently the highest they've been since his first year in office).
What is clear to me, though, is that the drive to impeachment cost Republicans in the 1998 mid-terms, leaving Bush with narrow majorities to push his programs through Congress.
And then Trump lost by more than Romney! His opponent taking a larger vote share than Reagan himself. Hmmm.