Make the documented docstring and README examples executable

[tschm]

Subcategory: executable documentation
Score: 4 → 9

Problem

The package documents examples nobody verifies. interrogate reports 100%
docstring coverage (63/63) — but coverage measures whether a docstring exists,
not whether what it claims is still true.

Six ​```python example blocks live in src docstrings:

• src/pycharting/api/interface.py — 3 (in plot, stop_server, get_server_status)
• src/pycharting/core/server.py — 2 (incl. find_free_port)
• src/pycharting/__init__.py — 1

All six are markdown fences rather than >>> doctests, so doctest never sees
them. The template's own check agrees, by skipping:

SKIPPED [1] .rhiza/tests/sync/test_docstrings.py:123: No doctests were found in any module

The README is the same story: of 7 Python fences, 6 carry +RHIZA_SKIP
(lines 78, 107, 139, 174, 219, 229), leaving exactly one machine-verified
Python example in the entire project.

This is the failure with the longest half-life in a repo — an example goes stale,
keeps rendering perfectly, and the person who finds out is a newcomer at the
worst possible moment.

Files to change

• src/pycharting/api/interface.py (docstrings of plot, stop_server, get_server_status)
• src/pycharting/core/server.py (docstrings of find_free_port, create_app)
• src/pycharting/__init__.py (module docstring)
• README.md — review the 6 +RHIZA_SKIP fences and un-skip those that can run

done when

• The src docstring examples are >>> doctests with expected output.
• make rhiza-test runs .rhiza/tests/sync/test_docstrings.py instead of
  skipping it with "No doctests were found in any module".
• uv run python -m doctest (or --doctest-modules in the pytest run) passes.
• Each remaining +RHIZA_SKIP in the README is justified by a comment saying why
  that example cannot execute (e.g. it starts a browser).

Evidence

check_doc_examples.py --source-root src --json:

"docstrings": { "files": 10, "examples": 0,
  "notes": ["no doctest examples found — docstring coverage says nothing about
             whether the docstrings are true, and here there is nothing to check"] }

Found by /rhiza:quality (full mode, rhiza v0.18.8).