feat: add check_exist tool

SYNO.FileStation.CheckExist returns error 400 for every parameter format on
this DSM firmware, so the tool falls back to SYNO.FileStation.List::getinfo.
DSM returns an entry per requested path with name=None for non-existent paths,
which provides a reliable exists/not-exists signal.

Accepts a single path or a comma-separated list; returns a table of
Path | Exists (Yes/No) with a count footer.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/mcp_synology_filestation/tools/filestation.py

@@ -538,6 +538,63 @@ def register_filestation(
 
         return "\n".join(lines)
 
+    @mcp.tool()
+    async def check_exist(path: str) -> str:
+        """Check whether one or more files or folders exist on the NAS.
+
+        Accepts a single path or a comma-separated list of paths.
+        Use share paths as returned by list_shares (e.g. "/dev/file.txt").
+
+        Note: SYNO.FileStation.CheckExist returns error 400 on this firmware for all
+        parameter formats. This tool falls back to SYNO.FileStation.List::getinfo, which
+        returns an entry per path with name=None when the path does not exist.
+
+        Args:
+            path: One or more share-relative paths, comma-separated
+                  (e.g. "/dev/notes.txt" or "/dev/notes.txt,/data/photo.jpg").
+
+        Returns:
+            Formatted table with each path and whether it exists (Yes / No).
+        """
+        from mcp_synology_filestation.client import SynologyError
+
+        paths = [p.strip() for p in path.split(",") if p.strip()]
+        if not paths:
+            return "Error: no path provided."
+
+        try:
+            data = await client.request(
+                "SYNO.FileStation.List",
+                "getinfo",
+                params={
+                    "path": json.dumps(paths),
+                    "additional": json.dumps([]),
+                },
+            )
+        except SynologyError as e:
+            return f"Error: {e}"
+
+        files: list[dict] = data.get("files", [])
+        if not files:
+            return "No information returned for the given path(s)."
+
+        # A path that doesn't exist still gets an entry but with name=None
+        rows = [(f.get("path", ""), "Yes" if f.get("name") is not None else "No") for f in files]
+
+        w_path = max(len("Path"), *(len(r[0]) for r in rows))
+        w_exists = len("Exists")  # "Yes" / "No" always shorter
+
+        sep = f"+{'-' * (w_path + 2)}+{'-' * (w_exists + 2)}+"
+        header = f"| {'Path':<{w_path}} | {'Exists':<{w_exists}} |"
+
+        lines = [sep, header, sep]
+        for item_path, exists_str in rows:
+            lines.append(f"| {item_path:<{w_path}} | {exists_str:<{w_exists}} |")
+        lines.append(sep)
+        lines.append(f"\n{len(rows)} path(s) checked.")
+
+        return "\n".join(lines)
+
     # ── write tools ───────────────────────────────────────────────────────
 
     @mcp.tool()