Notice broken sessions in the bar, and offer to repair them there

Nothing tells you a session is unresumable until you try to resume it, and by
then you have usually forgotten which one it was. The widget now scans every
project on a timer and whenever the panel opens, marks its icon when something
needs fixing, and lists the affected sessions with a repair button that says
what it will drop and what it will keep before doing anything.

The scan had to get roughly eighty times cheaper first. Classifying a transcript
needs two facts - what its last message id is, and whether any Anthropic id
exists at all - and the first settles the common case alone. Reading the tail of
each file and only opening the whole thing when the tail already looks wrong
takes the sweep from ~5s to ~60ms across 59 transcripts, which is the difference
between something that can sit on a timer and something that cannot. `--all`
uses the same path, and `--json` exposes it.

The badge is a dot beside the mark rather than a recolouring of it: this widget's
job is to report which provider is active, and tinting it red to mean something
else entirely would be a lie about that.

Verified by planting a genuinely corrupted transcript, watching the scan find it
and the dot appear, then removing it and watching both clear.

README.md

@@ -388,6 +388,23 @@ session untouched.
 It refuses to touch a transcript written to in the last 90 seconds, since that
 one belongs to a session still alive.
 
+### The bar notices for you
+
+Nothing tells you a session is unresumable until you try to resume it, by which
+point you have usually forgotten which one it was. So the widget scans every
+project on a timer (and whenever the panel opens) and puts a dot on its icon
+when there is something to fix. Clicking through lists the affected sessions and
+offers to repair each one, after saying what it will drop and what it will keep.
+
+The dot is a dot rather than a colour change, because recolouring the mark would
+misreport the active mode — which is the widget's actual job.
+
+That scan is only affordable because it reads the *tail* of each transcript
+first: if the last message is Anthropic's, the transcript is healthy and the
+rest of the file is never opened. Since that is the overwhelmingly common case,
+the whole sweep costs ~60ms for 59 transcripts, against ~5s for the obvious
+version that reads every byte of every one.
+
 This is why a switch now asks before it writes rather than reporting afterwards.
 So restart affected sessions — and `claude-mode sessions --restart` will do it
 for you: