I tiled our whole shower in honed and filled travertine, and its been good as gold.
Sealed with Lithofin which does a good job.
Mind you, I would only have done it with honed and filled so you don’t get the holes.
Tiled a shower with the tumbled travertine and all you do is seal the tiles first, then grout the entire face of the tiles which does fill the pitted areas.
Then seal again with at least two coats.