The idea was to add a shower there, value add for the home and guests wouldn't have to travel upstairs to shower.

There's a lot of dead space.

I would do something like this: https://imgur.com/a/HaAK2Ca

Like never before? I guess you didn't know about AllTrails.com

Wood filler like ProBond. Over fill it, shape it/sand it, paint

That contracts over time, not a good solution

Framing is correct for an interior wall with no load

https://www.buildingcode.online/1848.html

For insulation, you need to add exponentially more for it to make a difference. Basic insulation should achieve 90% heat retention. Doubling that gets you to 94% and returns diminish from there.

I would just air gap it

Let twitter die the death it deserves

Nature's Miracle Dog Urine Destroyer.

It's a concentrated enzyme that naturally breaks down the urine rapidly.

It's not cheap though, so training the dog to go on command should be key. If it's a large dog a walk at least every 8 hours is required. If it's a small dog, much more frequently.

It's obviously too wide for a transition. The best way to solve this is to fill it. You'll never match the edges/colour so don't try.

Personally, I would install a marble threshold or a [tile mosaic] (https://atlastile.com/wp-content/uploads/2020/01/tile-accent-border.jpg). That would let you use grout to hide the imperfect edges on the floor and get the height right.

Don't fill the hole. Caulking over top or a transition but that gap is needed for expansion of the floor.

You should try it with buttermilk