Store and compare file mtimes to the nanosecond (closes #226)

The files table held mtime in whole seconds and the scanner compared
whole seconds. A file rewritten with its size unchanged and a new mtime
in the same second as the indexed one was treated as unchanged, and
every later snapshot restored the old content. A new mtime_nsec column
now holds the nanoseconds within the second that mtime holds, and the
scanner compares the full mtime.

A local index created before this change lacks the column and is
rebuilt with `vaultik database delete` and a full backup. A snapshot
made before it cannot be restored by this version.

Model: opus-5-5

TODO.md

@@ -22,6 +22,16 @@ the tag exists and is exercised; what is left is merging `next` to
 
 # Completed Steps
 
+- 2026-10-07: Made a backup notice a file rewritten with its size
+  unchanged and a new mtime in the same second as the one in the index
+  ([issue #226](https://git.eeqj.de/sneak/vaultik/issues/226)). The
+  `files` table held mtime in whole seconds and the scanner compared
+  whole seconds, so every later snapshot kept the old content. A new
+  `mtime_nsec` column holds the nanoseconds within the second that
+  `mtime` holds, and the scanner compares the full mtime. A local index
+  created before the change lacks the column and is rebuilt with
+  `vaultik database delete` and a full backup.
+
 - 2026-10-07: Made taking the process-wide lock atomic
   ([issue #227](https://git.eeqj.de/sneak/vaultik/issues/227)). The lock
   read `vaultik.pid`, checked whether that PID was alive and then wrote