Epoxy is the "Gold Standard" for what you want. It is also expensive and requires some expertise to apply properly. I prefer the urathane premixed grout. About $70 a gallon, but far easier to use and is very close to epoxy in terms of durability. It's all I use on shower floors.

I used an epoxy grout in our laundry room because my wife was leery of cleaning grout. I paid a lot for most of it from the place where we bought the tile we liked. Then I found it cheaper in smaller containers (quart instead of gallon) at a local big box store and went with that when I had to fix the problems my installer had when I didn't order enough at first. That place only had gallons. I can tell you it is some work because you have to work fast but I was able to do the regrouting successfully myself.

We used epoxy grout in lots of our tiled rooms (and one shower). It's a LOT more expensive than regular grout, but regular grout is pretty dirt cheap, like $20 buys enough to do a whole large room. So it won't break the bank or run the tab way up, but you may spend $100 instead of $20 on materials.

I DIY'ed it successfully. It's a different process to apply and clean off the excess, but it's not rocket science and I had no problems. It does set up in the bucket faster, and I worked around that by mixing up a batch, putting 1/3 into a smaller container to use and storing the remaining 2/3 in the freezer to slow the curing. Then I'd take out another 1/3 and so on, so I could use it over a longer period of time (a couple hours, not a couple days or anything).

People say it takes longer to clean the epoxy grout, but to be honest for me it was about the same. It may be because the epoxy grout sets up faster, so there's less residual that comes out of the cracks when you wipe it down. With regular grout, I find myself wiping more times, because I always seem to trail out a bit of sand with each wipe and have to go back "one more time" to clean it all off.