Can someone tell me what problem this solves?
Well, first, forget the "all-new OS" nonsense - we're talking about a new user interface and application framework - plus, of course, these days an "operating system" involves a full supporting chorus of web browsers, media players, email & messaging clients, photo apps and probably a basic office suite of some sort, all using the appropriate UI and application conventions.
...and the problem is that different types of devices need different types of user interface. Phones have small screens and are entirely touch-driven while held in one hand. An Apple TV is designed to be operated by a remote control with only half a dozen buttons and the UI needs to be easily visible from 10' away (its actually known as a 10' UI). Macs have larger screens, are driven by trackpad/mouse and a physical keyboard. They may look grossly similar but if you actually try and design something non-trivial to work on both touch and keyboard/pointer you'll see the difference. For example - a mouse/trackpad lets you point at something quite precisely before you click. A touch screen is far less accurate (unless you use a stylus) and the system doesn't know where you're pointing until you actually touch it - which usually initiates an action. If that sounds pedantic, compare how you select/edit text on iOS vs. MacOS. Doing
anything with text entry on an Apple TV is like kicking a dead whale along a beach so it needs to be avoided...
The point is that you
can write one UI, one App that is usable across laptop/desktop/phone/tablet but it's not going to take full advantage of either medium, unless you go to great effort to make a fully adaptive/responsive UI. So much better if the key applications and utilities are designed specifically for the appropriate medium.
I did have a just-pre-iPhone Windows Mobile phone and the UI was a complete dumpster file, because the phone had (deep breath) a matchstick stylus, a small slide-out QWERTY keyboard, a "joypad", a jog/click wheel and function buttons on every surface... you had to try and decide which one of those worked best with whichever bit of software you chose (not that it woukd run actual Windows software - but what software it had used a windows-like UI). One of the key attractions of the iPhone was that everything had been designed from the ground up for a touchscreen-only device and
just worked.
The other horror story that Apple probably want to avoid is Windows 8 and the "Metro" user interface that (basically) tried to design a UI/App framework that would work on both laptop/desktop, tablet and phone - it failed. Frankly, I thought it showed promise as a phone UI, but nobody wanted a MS/Intel phone by then and it was horrific on a laptop.
The much maligned Appl Vision Pro is mainly an effort to create user interfaces suitable for doing
actual productivity work (rather than catching Pokemon or shooting aliens) using AR, head/eyball tracking, 3D hand gestures etc. A warmed-over desktiop UI running warmed-over desktop software isn't going to cut it.
So, the Watch - different uses, different UI requirement, different UI/Application framework required.
iPad - literally a half-way house between phone and laptop - iOS was too limiting for a large-screen iPad, MacOS would be unusable without a keyboard and trackpad (which turns the iPad from a great mobie device into a lousy laptop)
Presumably they've now decided that a Home Assistant needs a new UI - presumably to cope with a mixture of voice and a big-button UI.