Looks like you made an excellent choice!
I also wanted to chime in to add some additional thoughts for anyone else who might be considering something like the collapsible stool you had asked about initially. I have a stool like this but not to use as a shower stool; mostly I use it my kitchen or while doing chores if I don't have another seat immediately available to me. It's been a great little tool in those situations, but I wouldn't recommend it as a shower stool for two reasons:
1. It is really only functional if on a completely flat surface, and a lot of tubs and showers either have sloped sides or a mild slope or incline towards the drain, etc. So, even if it being wet/slippery wasn't also a concern, I'm not sure if would be very stable in a tub or shower.
2. Because of how the pieces interlock, the use of springs internally, and no way to really access the inside of the stool, it would be very hard to keep functional for the long-term. I would be concerned about the springs rusting and it would also be very hard to clean any shampoo, conditioner, soap, shaving cream, etc. that potentially got into the little crevices or even the inside of the stool.
I think the one you ended up picking makes a ton of sense. I've also used a sturdy, fold-able step stool with rubber grips on the bottoms of the legs in a pinch as a makeshift shower stool while travelling -- not medical advice and try it at your own risk, but it has worked well for me when another option was not easily available, especially the ones that are more mid-end as they often come in different heights/sizes that are comparable to what a shower stool would be
