feat: add ext: operator for file extension filtering in advanced search

- Add ext: operator support to query parser in backend and frontend
- Update search documentation in README and help modal with ext: examples
- Parse ext: operator to extract file extension filter (strips leading dot, converts to lowercase)
- Filter search candidates by file extension in advanced_search function
- Add ext chip display in search UI alongside existing tag/vault/title/path chips
- Update API documentation and function

backend/main.py

@@ -1636,15 +1636,14 @@ async def api_tree_search(
                     "path": entry["path"],
                     "name": entry["name"],
                     "type": entry["type"],
-                    "matched_path": entry["path"],
                 })
-    
+
     return {"query": q, "vault_filter": vault, "results": results}
 
 
 @app.get("/api/search/advanced", response_model=AdvancedSearchResponse)
 async def api_advanced_search(
-    q: str = Query("", description="Advanced search query (supports tag:, vault:, title:, path: operators)"),
+    q: str = Query("", description="Advanced search query (supports tag:, vault:, title:, path:, ext: operators)"),
     vault: str = Query("all", description="Vault filter"),
     tag: Optional[str] = Query(None, description="Comma-separated tag filter"),
     limit: int = Query(50, ge=1, le=200, description="Results per page"),
@@ -1659,6 +1658,7 @@ async def api_advanced_search(
     - ``vault:<name>`` — filter by vault
     - ``title:<text>`` — filter by title substring
     - ``path:<text>`` — filter by path substring
+    - ``ext:<type>`` — filter by file extension
     - Remaining text is scored using TF-IDF with accent normalization.
 
     Results include ``<mark>``-highlighted snippets and faceted tag/vault counts.