refactor(search): make PUBLIC_FIELDS a tuple[FieldSpec, ...], drop PublicField

PublicField duplicated seven fields whoosh-compat's own FieldSpec already
has (name/kind/aliases/comma_values/date_only/fast/subpaths), and
_registry.py hand-copied all of them across on every registry build.
FieldSpec is a frozen dataclass with analyzer/pattern_normalizer already
optional (default None), so PUBLIC_FIELDS can just BE the FieldSpec tuple -
_schema.py only ever read name/kind/fast off it and needs no changes.
_registry.py now attaches the per-language analyzer/pattern_normalizer via
dataclasses.replace() instead of reconstructing every field from scratch.

FieldSpec.__post_init__ normalizes subpaths into a MappingProxyType, so
test_fields.py's exact-tuple-equality subpath assertions become set
comparisons; a genuinely empty subpaths is now `not field.subpaths` rather
than `== ()`.

Verified test_api_trash.py::test_api_trash's "Schema error: An index exists
but the schema does not match" failure is a pre-existing, unrelated local
environment issue (a stale, untracked data/index/ directory in this
checkout) - reproduces identically with this commit's changes stashed out.

src/documents/tests/search/test_fields.py

@@ -20,7 +20,7 @@ class TestPublicFields:
     def test_non_json_fields_have_no_subpaths(self) -> None:
         for field in PUBLIC_FIELDS:
             if field.kind is not FieldKind.JSON:
-                assert field.subpaths == ()
+                assert not field.subpaths
 
     def test_document_type_alias_is_type(self) -> None:
         field = next(f for f in PUBLIC_FIELDS if f.name == "document_type")
@@ -36,11 +36,11 @@ class TestPublicFields:
 
     def test_notes_subpaths(self) -> None:
         field = next(f for f in PUBLIC_FIELDS if f.name == "notes")
-        assert field.subpaths == ("user", "note")
+        assert set(field.subpaths) == {"user", "note"}
 
     def test_custom_fields_subpaths(self) -> None:
         field = next(f for f in PUBLIC_FIELDS if f.name == "custom_fields")
-        assert field.subpaths == ("name", "value")
+        assert set(field.subpaths) == {"name", "value"}
 
     def test_no_internal_id_fields_present(self) -> None:
         # tag_id/owner_id/viewer_id/etc. are permission-filter-only fields,

src/documents/tests/search/test_schema.py

@@ -130,7 +130,7 @@ class TestSchemaMatchesPublicFields:
 
 class TestFastFlagAgreement:
     def test_every_public_field_fast_flag_matches_the_built_schema(self) -> None:
-        # whoosh-compat's registry trusts PublicField.fast when resolving
+        # whoosh-compat's registry trusts PUBLIC_FIELDS' fast flag when resolving
         # field:* existence checks (its FAST_FIELD strategy); a fast=True
         # entry whose actual tantivy column is not fast would make those
         # searches silently match nothing at search time. build_schema()
@@ -144,6 +144,6 @@ class TestFastFlagAgreement:
         }
         for public_field in PUBLIC_FIELDS:
             assert schema_fast[public_field.name] == public_field.fast, (
-                f"{public_field.name}: PublicField.fast={public_field.fast} but the"
+                f"{public_field.name}: PUBLIC_FIELDS says fast={public_field.fast} but the"
                 f" built schema says fast={schema_fast[public_field.name]}"
             )