Honestly, given the situation, I would NOT want glass walls or doors. I would get a shower curtain, put it on a curved rod, add a liner curtain, and be thankful that no one is going to get injured bumping into glass. Sometimes beauty and looking good has to defer to safety. The curtained shower will be much easier to clean, and it will be easier to wash large pets with this solution. I would be sure to have a handheld shower for the pets.

I didn't know you had sidelights. Are they fixed or can you open them? If the former you can use a handsaw and just cut out the portion of the threshold that is actually under the door itself. The sections under the sidelights are most likely nailed down, so you'd have to remove the sidelights to get at them. Probably something you'd want to avoid if you can. If you decide to cut out the threshold under the door only, use it as a template to cut the new threshold, but remember to cut the new one a little longer; about twice the thickness of the saw blade that you used to cut out the old. Hope this helps!

Both Polyshades and Varathane are light-duty finishes that won't wear well; that's how I read the 'not for floors' warning. Because a threshold sits above floor level it's prone to more scuffing of shoes than any other part of the floor (except, perhaps, the nosing of stair treads), and should have the toughest possible finish. I would stain yours to the appropriate color - Minwax stains are widely available and can work fine, but others are good too. I don't use a lot of stain in my work, but I've had good luck with Sherwin Williams'. Anyhow, once the stain has dried I would apply three coats of polyurethane, allowing each to dry and sanding lightly between coats.

Thank you @Phonenix Home Services. Still evaluating option there will be a double sliding door (2,60 height) between one sleeping room and the living. don't know if the other doors should have two bosses in the doors and/without additionally kind of greek frame on the top. Or much simpler sleek look meaning all flat.