Give both summaries a modified time, and the dashboard list a footprint

Home's "recently modified" order was a proxy — drafts first, then the
version counter, then the name. Both summaries now carry `updated_at`,
read as the mtime of the working copy: every write in the store commits
immediately, so a file's mtime is its commit time, and `git log -1 --
<path>` costs ~990ms across this instance's 15 documents (it walks the
history back to the last commit touching each one, so it is slowest for
the stalest) against ~1.8ms for the stats. No cache needed.

`DashboardSummary` also carries `footprint`: each widget as its type plus
the placement a panel resolves, which is the whole of what the mosaic
draws. That drops the document fetch per tile and with it the cap of
eight, past which tiles showed a name and nothing else. Verified against
this instance's 8 dashboards: the blocks are identical to what the old
client-side derivation produced.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01CL9zvnnvcp1mvA8o7impxk

backend/fluksio/flow/store.py

@@ -19,6 +19,8 @@ import logging
 import shutil
 import subprocess
 import threading
+from collections.abc import Iterable
+from datetime import UTC, datetime
 from pathlib import Path
 
 from fluksio.flow.schemas import FlowDef
@@ -84,6 +86,20 @@ class StaleVersion(ValueError):
         return f"Flow '{self.name}' has changed since you loaded it"
 
 
+def _updated_at(paths: Iterable[Path]) -> datetime | None:
+    """When the newest of these files was written, or ``None`` if none exist.
+
+    A file's mtime, not the commit that recorded it: every write here commits
+    immediately, so the two are the same instant, and `git log -1 -- <path>`
+    would walk the history back to the last commit touching that path — 130ms
+    for a document nobody has edited in a week, against a `stat` for all of
+    them. Slowest for exactly the stalest documents is the wrong shape for a
+    list endpoint.
+    """
+    stamps = [path.stat().st_mtime for path in paths if path.exists()]
+    return datetime.fromtimestamp(max(stamps), UTC) if stamps else None
+
+
 def _same_content(left: FlowDef, right: FlowDef) -> bool:
     """Equal but for the version counter, which the server owns."""
     return left.model_copy(update={"version": 0}) == right.model_copy(
@@ -386,6 +402,18 @@ class FlowStore:
         drafts = self._draft_nodes_dir(name)
         return drafts.exists() and any(drafts.glob("*.py"))
 
+    def updated_at(self, name: str) -> datetime | None:
+        """When this flow was last written — its document or any node's source.
+
+        Node code is saved without touching the flow document, so a flow whose
+        last change was to a node body would otherwise look untouched.
+        """
+        return _updated_at(
+            [self._flow_file(name), self._draft_file(name)]
+            + list((self._flow_dir(name) / "nodes").glob("*.py"))
+            + list(self._draft_nodes_dir(name).glob("*.py"))
+        )
+
     def read_flow(self, name: str, draft: bool = False) -> FlowDef:
         """The published flow, or with ``draft`` the working copy."""
         if draft: