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/search.py

@@ -534,19 +534,21 @@ def _parse_advanced_query(raw_query: str) -> Dict[str, Any]:
     - ``vault:<name>`` — vault filter
     - ``title:<text>`` — title filter
     - ``path:<text>`` — path filter
+    - ``ext:<type>`` — file extension filter
     - Remaining tokens are treated as free-text search terms.
 
     Args:
         raw_query: Raw query string from the user.
 
     Returns:
-        Dict with keys ``tags``, ``vault``, ``title``, ``path``, ``terms``.
+        Dict with keys ``tags``, ``vault``, ``title``, ``path``, ``ext``, ``terms``.
     """
     parsed: Dict[str, Any] = {
         "tags": [],
         "vault": None,
         "title": None,
         "path": None,
+        "ext": None,
         "terms": [],
     }
     if not raw_query:
@@ -568,6 +570,8 @@ def _parse_advanced_query(raw_query: str) -> Dict[str, Any]:
             parsed["title"] = token[6:].strip()
         elif lower.startswith("path:"):
             parsed["path"] = token[5:].strip()
+        elif lower.startswith("ext:"):
+            parsed["ext"] = token[4:].strip().lstrip(".").lower()
         else:
             parsed["terms"].append(token)
 
@@ -639,7 +643,7 @@ def advanced_search(
     sorted token list for O(log V + k) instead of O(V) linear scan.
 
     Parses the query for operators (``tag:``, ``vault:``, ``title:``,
-    ``path:``), falls back remaining tokens to TF-IDF scored free-text
+    ``path:``, ``ext:``), falls back remaining tokens to TF-IDF scored free-text
     search using the inverted index.  Results include highlighted snippets
     with ``<mark>`` tags and faceted counts for tags and vaults.
 
@@ -673,7 +677,7 @@ def advanced_search(
     query_terms = [normalize_text(t) for t in parsed["terms"] if t.strip()]
     has_terms = len(query_terms) > 0
 
-    if not has_terms and not all_tags and not parsed["title"] and not parsed["path"]:
+    if not has_terms and not all_tags and not parsed["title"] and not parsed["path"] and not parsed["ext"]:
         return {"results": [], "total": 0, "offset": offset, "limit": limit,
                 "facets": {"tags": {}, "vaults": {}}, "query_time_ms": 0}
 
@@ -725,6 +729,16 @@ def advanced_search(
             if norm_path_filter in normalize_text(inv.doc_info[dk].get("path", ""))
         }
 
+    if parsed["ext"]:
+        ext_filter = parsed["ext"]
+        candidates = {
+            dk for dk in candidates
+            if (
+                inv.doc_info[dk].get("path", "").rsplit("/", 1)[-1].lower() == ext_filter
+                or inv.doc_info[dk].get("path", "").rsplit("/", 1)[-1].lower().endswith(f".{ext_filter}")
+            )
+        }
+
     # ------------------------------------------------------------------
     # Step 3: Score only the candidates (not all N documents)
     # ------------------------------------------------------------------
@@ -774,7 +788,7 @@ def advanced_search(
                 for expanded_term in expansions:
                     score += inv.tf_idf(expanded_term, doc_key) * 0.5
         else:
-            # Filter-only search (tag/title/path): score = 1
+            # Filter-only search (tag/title/path/ext): score = 1
             score = 1.0
 
         if score > 0: