I have a room addition (built before I bought the house). It lacks connection to the central AC system.
Been using it mostly for storage until recently, where I turned it into a home office/Den/gaming room/Mancave
Problem is, it needs a Window AC unit.
There used to be one, because I can tell from looking at the wall that the wall had previously had a cut out for a Window unit, which was then patched over (badly). From the exterior, you can even see the cut outline, whereas inside its just badly plastered over.

The Outlet just below that, is a dedicated Circuit... so its good for use with AC.
Need to put an AC in.

Room is 12.5 feet by 12.5 feet.
3 Walls are exterior facing. 1 wall faces southbound, with a tiny window (not big enough to accomodate most ACs, and my wife definitely doesn't want me putting an AC in that window and insists on reopening the wall-hole).

How much BTU do you recommend for a room this size, in Arizona? I know when I look online, most recommendations seem to be 5000 to 6000 BTU for a room this size. But I fear that these recommendations are meant for most of the rest of the US and not the Phoenix Metro area's especially hot climate.
I had an AC professional come to my home to do some duct work repair in my attic, and after he finished, I asked him for a recommendation. He recommended 8000 BTUs. Does this sound about right? Or is that overkill?
I dont want my AC to "Short cycle".

Please don't try recommending Minisplit. Its only ONE small room, and a minisplit costs waaaay too much compared to what I can get a Window unit for.

The thing is, it mostly depends on insulation. A well insulated room won't take much at all, whereas if that was previously a patio and doesn't have any insulation... good luck.

For instance, I have a 2.5 ton unit to do my basement. That would be considered grossly undersized by most people in Phoenix metro looking at cooling ~1500SF. But it's a basement in a block house... it's fine. In fact, it barely runs until it gets up north of 100.

I suspect, based on most of what I have seen of Arizona construction, especially on additions, is that you don't have much, so it's probably better to go big. That said... You can get a cheap 5000BTU unit for $150. A bigger one costs significantly more. And the little guy will probably do the job, even if it's running balls to the wall and it gets a little warm in the summer.

One other option are portables. I have one, nominally for my Garage, but it's damn useful if someone's AC goes out while it's being replaced. (In the garage, it's just to keep ME cool, it can't cool the whole 3 car garage and I don't try to)

ETA:

That portable I have is 7-8000 BTU. It did a damn reasonable job when my upstairs (also about 1500 SF) AC had issues last summer. It wasn't 'cool' but it at least kept the house liveable... and that's WAY outside what it 'should' be able to do. That said, it never had to do it for more than a couple hours before the main AC kicked back on. (Problem was a float switch that took a bit to run down. Previous owners had wired it to kill the thermostat if there was water in the pan. It would get humid, start to make water, back up, and kill the thermostat... but then it would drain and start back up. Removing the bush that had found the drain line was what fixed it. )