Azek or other foamed PVC/wood flour products don't take on water like the wood will.

Replace the window with a vinyl window. Make sure the rough-in stool is sloped toward the tub 3-4 degrees is enough. Wrap Kerdi backer cloth into the window opening to seal any possible leaks. Tile up to the window over the Kerdi cloth.. Your contractor should know the detail of how this is done. We do it all the time. What are you going to do with the floor register? Why move the tuba at all? It looks nicely at home where it is. Moving it would be more work and expense than it is worth.

I currently have a casement window in my shower, and yes, it has a screen, and we do use it to vent after a shower. It is a vinyl casement and we trimmed it out (inside and out) with exterior composite trim material. My husband is a building contractor, and always mindful of issues. We towel down the trim EVERYTIME we shower, not so much for water rot worries, but for soap scum and water stains. Soap residue will show on any surface, whether or not the water air dries. It's great to have natural light in the shower, not to mention fresh air. Enjoy your shower window.

If outside people can see the window, I would close it up completely or below 5-6’ height. Or landscape in front of it so no one is tempted to look in. Window film is a temporary solution. Maybe outside shutters that close over the window could be an option. I had a neighbor who put frosted windows into his bathroom on the side of his house. The frosted film didn’t help. Once the light went on, TMI, even if just blurry shapes. People will look into bathroom windows from the street or sidewalk or their neighboring homes. It’s just too weird and the windows shouldn’t be there unless they are completely private or above shoulder level.