Migrate codebase to adopt explicit /schema entrypoints for Tool UI schemas.

Goals:
1) Move all schema helper imports to dedicated /schema entrypoints per component.
2) Keep public UI imports under their component paths; import schema only from /schema modules.
3) Update tests and docs to reflect new entrypoints and boundary semantics.
4) Regenerate artifacts (registry/public assets) and update docs accordingly.
5) Validate UI rendering with updated imports and schema contracts.

Steps:
- Replace imports of Serializable*Schema, parseSerializable*, and safeParseSerializable* from non-schema tool-ui entrypoints with imports from the component's /schema module (e.g., @/components/tool-ui/<component>/schema).
- For all affected components, update imports to reference /schema entrypoints; preserve existing UI imports.
- Update relevant tests and docs to reflect new entrypoints and boundary semantics.
- Run lint, typecheck, and tests; fix breakages.
- Regenerate artifacts (registry/public assets) and update docs accordingly.
- Validate UI rendering with updated imports and schema contracts.