I think your issue may be similar to this one OP.
When one person organises everything, books everything, decides everything in advance without consulting the other person, it can get really grating, I mean this kindly but you seem quite bossy op, you probably think you're just organised but that can come across as you being 'in charge' when you're away together, coupled with her being negative anyway it is a bit of a recipe for disaster.
From what you've said to her and what you've said about her is that you don't trust her to make decisions so instead you either decide and tell her what's happening or you give her options to choose from instead, it is quite infantilising and can prompt some people to revert to a petulant type of attitude because they aren't being treated like an adult. Almost like they are being treated like a child so they act like one. She may have thought she'd have more autonomy when it came to the holiday but as it happens you'd already decided what you were doing and when.
She should have told you that you were doing her head in, but maybe, ironically, she didn't want to ruin the holiday, and you ignoring it and pretending everything's okay didn't bring it to a head so you both just bumbled through it instead.
wait here
telling her to wait for you while you wanted to go off and sort something out, it's like dealing with a child not an adult capable of making decisions themselves.
… when if it was down to her it would never have been figured out.
referring to getting taxis instead of the metro and her response of why didn't we do this yesterday, this shows how you feel about her capabilities as an equal.
I booked us in for an hour (at the spa)
Again, just went ahead and booked it, she kicked off after you told her it was booked.
Which for reference she wouldn’t pick a place
Which actually means as you've clarified that you were only giving her options and she wouldn't pick one of your choices.
Thats why I also suggested me buying her a drink, there are so many different Aperol Spritz on the menu and the bar for anyone who doesn’t know has a balcony above the square overlooking the cathedral. You have to queue to get a seat but it’s not like we had to be somewhere. And she just wasn’t bothered.
Again, something you wanted to do, not her.
she said no we’ll walk, then she looked at me and said really aggressively “well I can tell by your face you don’t want to”
This is quite telling, after everything that's happened she wanted to do it a certain way (to save money) but you wanted it your way, you had good reason, but it sounds like a long line of doing things that you wanted, she'd had enough at this point.
I said 'wait for me near these stairs'
again, you telling her what to do instead of asking her.
You're actually complaining and being frustrated that she didn't just do as she was told half the time, when really you shouldn't have been 'telling' her what to do at all, maybe she thought that when you got there you'd be able to make decisions together about what you wanted to do but it became clear that you wanted to be in charge and she was just expected to traipse around after you for the few days. You're obviously very different people and not holiday compatible.