Share Lean-derived problem metadata across consumers

**Implementation: #5375.** Replace independently reconstructed facts with a shared Lean extraction boundary.

| Consumer | Shared input |
| --- | --- |
| Website and CLI browsing | Native `conjectures.json`: statements, categories, subjects, proof references and source provenance |
| Erdős status and proof-link checks | The same published metadata, through consolidated #4828 |
| Native proof export | Shared semantic facts where applicable; exporter-specific elaboration and signature checks remain native in #5337 |

#5375 introduces `FormalConjecturesUtil/ProblemMetadata.lean` and keeps one published `conjectures.json`. Its versioned native schema and manifest make source revision and integrity explicit; rendering is separate. Consumers do not reconstruct missing metadata with source regexes or an old website projection.

Acceptance:

- [ ] #5375 is accepted and merged.
- [ ] Repeated extraction from the same pinned inputs preserves identical semantic data.
- [ ] Representative collections, variants, conditional proofs, quoted names and answer holes preserve their meanings across consumers.
- [ ] The published catalog supplies statements and matching provenance.

Fork qualification is recorded in #5375 and #5377; upstream publication is still pending. Categorized anonymous `example` declarations are not assigned invented persistent identities. Their policy is tracked separately in #4819.

The original motivation cited #4951's Python reconstruction. That approach is superseded by #5337; it is not a consumer to keep extending. Roadmap: #4394. Close this issue on #5375's merge after its acceptance checks.

Start with #5375 and FormalConjecturesUtil/ProblemMetadata.lean, then inspect the single published conjectures.json and its versioned schema and manifest. Use #5375's acceptance checks for repeated extraction and representative collections; done when #5375 merges and the catalog supplies statements with matching provenance.

Written by the indexing model from the issue text.