What changed

• Replaced local recursive form tree walkers with flattenSubtree from @core/page-tree.
• Replaced the editor form analyzer's derived child-scan parent map with getParent, using the canonical parent index maintained by page-tree parsing/mutation boundaries.
• Added an architecture regression to prevent these form modules from reintroducing local tree-walk/parent-map helpers.
• Updated form analyzer fixtures to stamp parentId via reindexNodeParents, matching the production page-tree invariant.

Why

Form publishing and editor-side form settings had their own tree traversal and parent lookup implementations. That duplicated logic bypassed the cycle-safe page-tree selector path and obscured the parentId source-of-truth invariant.

Impact

Form snapshot generation and form settings analysis now depend on the same page-tree selector primitives as the rest of the editor engine. The form-specific inference behavior is unchanged and covered by existing tests.

Verification

• bun test src/__tests__/architecture/page-tree-single-source.test.ts red before implementation, then passing
• bun test src/__tests__/forms/formSnapshot.test.ts src/__tests__/forms/formSettingsAnalysis.test.ts
• bun run build
• bun test
• bun run lint