Lots of varying questions.
What is going on with Apple’s so-called "factory calibration"? It is completely inconsistent across devices. I own five different Apple devices, and every single display shows a different color tone.
What's "going on" is you have five different devices. Each has its own display panel, graphics hardware, version of Apple's OS, even different versions of ColorSync (and whatever iOS devices use under the hood). They simply aren't going to match out of the box.
And like literally any display panel (stand-alone monitor, all-in-one computer, tablet, etc.), they all come with one supplied profile based on one device someone created a profile for. That profile is then embedded in every single device that is the same model. Doesn't matter that it isn't all that accurate, or even the gray balance you want. It's a relatively decent starting point, and nothing else.
My Mac Studio Display came with a noticeable tint - luckily, I managed to somewhat fix it at the macOS level using my Calibrite Display Plus-HL.
Good, which is the very first thing any color professional should do - create real profiles made from a hardware calibration package.
My iPhone 15 Pro now looks closer to the Studio Display … More importantly, ColorSync does absolutely nothing for the iPad Pro M5.
When it comes to on-screen color, Pro means nothing in iOS, which is an entirely locked down system. You cannot in any way create your own display profiles for iPads or iPhones. That would require access to the system, which is 100% off limits. Not the Pro means nothing. The Pro iOS devices have far, far better color rendering for both stills and video than the non-pro versions. As long as you're always using ProRAW for stills, and Apple ProRes for video, that is. If you're not, color isn't very good.
As an example, I first upgraded from an iPhone 6s to a 14. The color, sharpness and overall quality was terrible. Going from a Nikon D800 to that was a serious letdown, since my goal was to sell all of my pro gear and just use a good phone. I'd seen enough sample images and videos though to have a good idea what was wrong. And that was simply the small cost difference between the 14 and 14 Pro. Sent the regular 14 back and got the Pro. HUGE difference in image and video quality.
But the main point is, with iPads and iPhones, no matter what model or how much you spent on them, the screen color is out of your control. You can only set brightness and an overall tone between yellow and blue. I set my 14 Pro so it closely matches the gray of an EIZO monitor calibrated and profiled to D50. Then I just leave it there. It isn't perfect, but it's decent.
But my MacBook Pro 16 M1 has a completely different color cast.
Same as above. Different display panel, graphics hardware, etc. It's not going to match your Studio Display until you properly profile and calibrate it with your Calibrite Display Plus-HL to the same settings. And even then, while you should be able to match the gray balance from one to the other, they still won't look exactly the same. Different panels, different appearance.
I calibrated the Studio Display using the built-in macOS display calibration tool.
Calibrating any display by eye is an utter waste of time. The OS does not know what you're looking at, so the resulting profile means nothing to ColorSync. And besides, this is the opposite of, I managed to somewhat fix it at the macOS level using my Calibrite Display Plus-HL. Sooooo, did you eyeball the color on the Studio Display, or did you properly calibrate/profile it with the Plus-HL?
And this isn't just an Apple thing. There's no image or video capture device (including multi-thousand dollar studio cameras) that don't need to be color managed. Every single device that displays, captures or prints color requires its own profile since each one is its own little island of color rendering specific hardware and software.
I understand the frustration of iPads and iPhones, but they just aren't meant to be color accurate displays. Mainly because you cannot profile them. You get them looking as close to a natural gray balance as you can, and correct the images and video you shoot with them as necessary afterwards.