Make `Base.depwarn()` public (#55212)
There's a few reasons for making it public:
- It's already mentioned in the manual (#54211).
- It's the easiest way to deprecate a function that shouldn't be used
anymore at all.
- It's already widely used in the ecosystem:
https://juliahub.com/ui/Search?type=code&q=Base.depwarn(
I also moved the `@deprecate` docs into a new `Managing deprecations`
section because I felt it should go together with `Base.depwarn()`.
Might be worth backporting to 1.11?
