[3.13] gh-124872: Refine contextvars documentation (GH-124773) (#125233)

[3.13] gh-124872: Refine contextvars documentation (GH-124773) (#125233)

[3.13] gh-124872: Refine contextvars documentation

  * Add definitions for "context", "current context", and "context
    management protocol".
  * Update related definitions to be consistent with the new
    definitions.
  * Restructure the documentation for the `contextvars.Context` class
    to prepare for adding context manager support, and for consistency
    with the definitions.
  * Use `testcode` and `testoutput` to test the `Context.run` example.

(cherry-picked from commit 99400930ac1d4e5e10a5ae30f8202d8bc2661e39)

Co-authored-by: Carol Willing <carolcode@willingconsulting.com>