Post-release followups for 4.16.0rc1

[AlexWaygood]

• Add some missing things from the changelog w.r.t. things we changed between 4.15 and 4.16.0rc1
• Spruce up a few details in the docs regarding things we changed between 4.15 and 4.16.0rc1
• Officially declare support for Python 3.15 in pyproject.toml
• Add a note to CONTRIBUTING.md reminding future maintainers to check the CHANGELOG before releasing things
• Bump the version in pyproject.toml to 4.16.0rc1.dev, per the CONTRIBUTING guidelines here: https://github.com/python/typing_extensions/blob/main/CONTRIBUTING.md#workflow-for-pypi-releases

I'll edit the changelog updates here into the GitHub release after this PR lands.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.26%. Comparing base (777de3e) to head (8d04657).

@@           Coverage Diff           @@
##             main     #767   +/-   ##
=======================================
  Coverage   97.26%   97.26%           
=======================================
  Files           3        3           
  Lines        7862     7862           
=======================================
  Hits         7647     7647           
  Misses        215      215           

Flag	Coverage Δ
3.10	88.85% <ø> (ø)
3.10.4	88.85% <ø> (ø)
3.11	88.03% <ø> (ø)
3.11.0	87.28% <ø> (ø)
3.12	87.97% <ø> (ø)
3.12.0	87.96% <ø> (ø)
3.13	83.39% <ø> (ø)
3.13.0	84.11% <ø> (ø)
3.14	79.54% <ø> (ø)
3.9	89.54% <ø> (ø)
3.9.12	89.54% <ø> (ø)
pypy3.10	88.69% <ø> (ø)
pypy3.11	87.89% <ø> (ø)
pypy3.9	89.37% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.