Nope, you’re definitely wrong as far as Ubuntu goes, which merely suggests that package, but does not require it: Ubuntu – Details of package gnome-shell in jammy
Since Ubuntu is the base for a LOT of other distributions, that means they all don’t come with Extensions by default, unless the maintainers specifically change that.
No, I mean the Extension Manager. First of all, the Extensions app is written in JavaScript, while the Settings app is written in C, which would likely make the integration rather difficult if not impossible.
Second, the Extensions app by itself is fairly useless without a simple way to install extensions. And like I said, doing that via the browser is fairly awkward, unless you also install a browser extension. Which is only available for Firefox and not for Epiphany, so that basically all but requires Firefox to be installed to even be useful.
Compared to that, having a software browser in the Settings app seems far less awkward, especially because this “browser” is quite limited and focused, and not particularly complex:
Also, the Extensions Manager is written in C, so it would likely be much easier to integrate into Settings.
No. I skipped the tour and I don’t read help files, because it’s usually faster to find solutions online. I WOULD have found it if it was integrated into the Settings app, though.