Incorporated EP2025 sprint feedback and added a new section

[agronholm]

Changes

This:

• updates the PyPI short description
• improves the documentation based on the feedback from the EuroPython 2025 sprints
• adds a new section explaining why one would want to use AnyIO's APIs instead of asyncio's
• fixes a number of broken documentation links

Checklist

If this is a user-facing code change, like a bugfix or a new feature, please ensure that
you've fulfilled the following conditions (where applicable):

• You've added tests (in tests/) added which would fail without your patch
• You've updated the documentation (in docs/, in case of behavior changes or new
  features)
• You've added a new changelog entry (in docs/versionhistory.rst).

If this is a trivial change, like a typo fix or a code reformatting, then you can ignore
these instructions.

Updating the changelog

If there are no entries after the last release, use **UNRELEASED** as the version.
If, say, your patch fixes issue #123, the entry should look like this:

- Fix big bad boo-boo in task groups
  (`#123 <https://github.com/agronholm/anyio/issues/123>`_; PR by @yourgithubaccount)

If there's no issue linked, just link to your pull request instead by updating the
changelog after you've created the PR.

[agronholm]

I still have more changes incoming, hence the draft status.

[davidbrochart]

Should Trio be upper-case everywhere?

[agronholm]

Should Trio be upper-case everywhere?

I believe it already is?

[davidbrochart]

Not in the README.

[agronholm]

Alright, I fixed that one occurrence now.

[davidbrochart]

I still see two occurrences.

[agronholm]

Fixed.