What

pn doctor gains a --json flag for scripting, mirroring pn devices --json (#22). With --json, stdout carries a JSON array of check results and nothing else; the human verdict line moves to stderr. Exit codes are unchanged — still keyed to the worst check level.

Nothing changes for the default invocation: pn doctor without the flag prints the same report it always has.

Why

• Tooling and CI that want to gate on toolchain health had to parse formatted, alignment-padded text. pn devices already solved this with --json; pn doctor should match.
• Keeping stdout pure JSON and pushing the verdict to stderr means pn doctor --json | jq works without a filter step, the same contract pn devices --json uses.

How (brief)

src/pythonnative/project/doctor.py

• Add CheckResult.to_dict() returning {"name", "level", "message"}. The dataclass field is detail; it's exposed as message in the payload since that reads better for a consumer and is what the issue asked for.

src/pythonnative/cli/pn.py

• Add --json to the doctor subparser (action="store_true"), wording modelled on the devices parser.
• doctor_command computes worst_level once, then branches: --json prints json.dumps([r.to_dict() for r in results], indent=2) to stdout and the verdict to stderr; the report path is unchanged except the verdict now goes through the shared helper. sys.exit(1) on ERROR is a single tail statement for both paths.
• Extract _print_doctor_summary(level, stream) so the three verdict strings can't drift between the report and --json, the same pattern as _print_no_devices_hints(stream) for pn devices.
• Update the module docstring's pn doctor line.

tests/test_cli.py

• Four tests following the pn devices --json tests: JSON array parses with keys {name, level, message}; report header/verdict kept off stdout with the verdict on stderr; ERROR still exits 1 with the verdict on stderr; --json wired through argparse via a real pn init project driven by run_pn.

tests/project/test_doctor.py

• Unit test for CheckResult.to_dict(), including the empty-detail default.

docs/api/cli.md

• pn doctor bullet documents --json: JSON array to stdout, verdict to stderr, exit status unchanged.

Testing

• ./scripts/check.sh passes (ruff, black, mypy, pytest, e2e coverage).
• New doctor tests: 17 pass (13 in test_doctor.py, 4 in test_cli.py).
• The 4 test_cli_init_rejects_symlinked_target failures on Windows are pre-existing (symlink creation needs admin privilege) and reproduce identically on main — unrelated to this change.

Risks/Impact

• Default pn doctor output and exit codes are unchanged; only the new flag adds behaviour.
• --json verdict text is identical to the report's, routed to stderr — safe for | jq and for scripts that only inspect the exit code.
• No dependency or API changes.

Docs/Follow-ups

• CLI reference (docs/api/cli.md) and the pn.py module docstring updated in this PR.

Closes #37