gen_providers_doc.py: add --check and run it in CI

[cunninghamcard-bit]

Part of #166; RFC-0033 §4.1 item 2.

Rule: a generator may stay in scripts/ only if its output carries a "do not edit" header and CI runs it with --check. gen_provider_names.py already complies (ci.yml line ~400). gen_providers_doc.py generates docs/api/providers.md but has no --check mode and CI never runs it, so the page drifts from provider_registry.json.

Work

• Add --check to scripts/gen_providers_doc.py (regenerate to a temp file, diff, non-zero exit on mismatch), matching the gen_provider_names.py pattern.
• Add a CI step next to the existing gen_provider_names.py --check.
• Regenerate docs/api/providers.md once so the first run is green.