fix(patch): gate 'did you mean?' to no-match + extend to v4a/skill_manage

Follow-ups on top of @teyrebaz33's cherry-picked commit:

1. New shared helper format_no_match_hint() in fuzzy_match.py with a
   startswith('Could not find') gate so the snippet only appends to
   genuine no-match errors — not to 'Found N matches' (ambiguous),
   'Escape-drift detected', or 'identical strings' errors, which would
   all mislead the model.

2. file_tools.patch_tool suppresses the legacy generic '[Hint: old_string
   not found...]' string when the rich 'Did you mean?' snippet is
   already attached — no more double-hint.

3. Wire the same helper into patch_parser.py (V4A patch mode, both
   _validate_operations and _apply_update) and skill_manager_tool.py so
   all three fuzzy callers surface the hint consistently.

Tests: 7 new gating tests in TestFormatNoMatchHint cover every error
class (ambiguous, drift, identical, non-zero match count, None error,
no similar content, happy path). 34/34 test_fuzzy_match, 96/96
test_file_tools + test_patch_parser + test_skill_manager_tool pass.
E2E verified across all four scenarios: no-match-with-similar,
no-match-no-similar, ambiguous, success. V4A mode confirmed
end-to-end with a non-matching hunk.

tests/tools/test_fuzzy_match.py

@@ -262,3 +262,70 @@ class TestFindClosestLines:
         # Should include line numbers in format "N| content"
         assert "|" in result
 
+
+class TestFormatNoMatchHint:
+    """Gating tests for format_no_match_hint — the shared helper that decides
+    whether a 'Did you mean?' snippet should be appended to an error.
+    """
+
+    def setup_method(self):
+        from tools.fuzzy_match import format_no_match_hint
+        self.fmt = format_no_match_hint
+
+    def test_fires_on_could_not_find_with_match(self):
+        """Classic no-match: similar content exists → hint fires."""
+        content = "def foo():\n    pass\ndef bar():\n    pass\n"
+        result = self.fmt(
+            "Could not find a match for old_string in the file",
+            0, "def baz():", content,
+        )
+        assert "Did you mean" in result
+        assert "foo" in result or "bar" in result
+
+    def test_silent_on_ambiguous_match_error(self):
+        """'Found N matches' is not a missing-match failure — no hint."""
+        content = "aaa bbb aaa\n"
+        result = self.fmt(
+            "Found 2 matches for old_string. Provide more context to make it unique, or use replace_all=True.",
+            0, "aaa", content,
+        )
+        assert result == ""
+
+    def test_silent_on_escape_drift_error(self):
+        """Escape-drift errors are intentional blocks — hint would mislead."""
+        content = "x = 1\n"
+        result = self.fmt(
+            "Escape-drift detected: old_string and new_string contain the literal sequence '\\\\''...",
+            0, "x = \\'1\\'", content,
+        )
+        assert result == ""
+
+    def test_silent_on_identical_strings(self):
+        """old_string == new_string — hint irrelevant."""
+        result = self.fmt(
+            "old_string and new_string are identical",
+            0, "foo", "foo bar\n",
+        )
+        assert result == ""
+
+    def test_silent_when_match_count_nonzero(self):
+        """If match succeeded, we shouldn't be in the error path — defense in depth."""
+        result = self.fmt(
+            "Could not find a match for old_string in the file",
+            1, "foo", "foo bar\n",
+        )
+        assert result == ""
+
+    def test_silent_on_none_error(self):
+        """No error at all — no hint."""
+        result = self.fmt(None, 0, "foo", "bar\n")
+        assert result == ""
+
+    def test_silent_when_no_similar_content(self):
+        """Even for a valid no-match error, skip hint when nothing similar exists."""
+        result = self.fmt(
+            "Could not find a match for old_string in the file",
+            0, "totally_unique_xyzzy_qux", "abc\nxyz\n",
+        )
+        assert result == ""
+