1: Be able to rotate stable tabs. For example, you could make tab 6 swap places with tab 1.

2: Be able to move stable tabs between stables. Ex: Move stable tab 4 to Stable #2. This would only work if there was open space for the tab, and the tab had already been paid for, of course.

3: "I also think it would be nice if shift-selecting was possible like if I selected the pet at the top of a tab and the pet at the bottom it would select all the pets in that tab, because I don't like having to click on every single pet I want to move if they are all in a clump together.
There's no harm in making minor changes if it would make the user experience better." (Firepepr)

you can basically do that already with the new stable functions, you just need to clear the tab first

Support, I think we should be able to drag the tabs around like in computer browsers, and being able to move between stables would be good as well.
I disagree that this can already be done. This would be much simpler and quicker than clearing a whole tab and then mass moving, plus I like having spaces between certain pets and mass moving smooshes them all together. I think there is always room for improvement and the stables should to be easier to use.
I also think it would be nice if shift-selecting was possible like if I selected the pet at the top of a tab and the pet at the bottom it would select all the pets in that tab, because I don't like having to click on every single pet I want to move if they are all in a clump together.
There's no harm in making minor changes if it would make the user experience better.

Oh, I didn't know that. I meant moving it with the pets in the tab though...

Yes! That is exactly what I meant :)

As for the shift selection, that would be amazing! Is it okay if I added your idea (with credit to you, of course) above?

Yes ofc! ^^

Thanks!