"My plan was to cut the “rotten” or water infiltrated part" You will find more water infiltration issues as you start to demo this. I would suck it up and do it over properly now before the structure rots further.

We live in a cold weather climate and have a skylight in the middle of our master bath ceiling. The bathroom is about 12 ft long. The shower is on one end and the exhaust fan is actually on the opposite end. In the 20 years that we have lived in this house, there has never been condensation forming on the skylight glass and dripping down the shaft. Maybe your exhaust fan is inadequate. We also have 2 skylights in our great room . The house is 33 years old. We did replace the roof and and all the skylights a couple years ago. No problem with previous skylights or current skylights dripping. They are flat glass skylights. We did use Velux brand skylights. Here is the bathroom set up. The exhaust fan is not shown but it is in the far right corner beyond the vanity and above the toilet. With all that being said, in our previous house we had a skylight in our kitchen that did collect condensation on the glass and it would drip down the shaft. I don’t recall what brand that skylight was. For a few years we would get up on a ladder and put 3M window film on the skylight in the winter months. It solved the condensation problem put was a pain in the butt to put up there. We finally had a storm window made and installed on the skylight. The "storm window" was attached on the inside. If my memory serves me correctly, it was a framed acrylic panel that was attached to the skylight. It solved the condensation problem and the problem with installing window film each winter. I hope you find a solution to your problem.

Your tile has seams. No reason to think that this is any different. Just change your perspective. It's not like you're trying to make it look like the entire shower was carved from a single block of stone, right? It's really pretty and nobody is going to ding you for having a seam.

No clue on thr type of grout, nor do i know if they sealed it. I assumed they would have, given that they renovate houses all the time with high end materials, but maybe that’s a bad assumption. Looking back thru other photos i received, it looks like they tiled this a couple months ago. So i’m just stuck with it like this? Can i try a poultice around the edges or something?