feat(S05/T02): Added an end-to-end trust-loop regression, surfaced save…

- job-tracker-ui/src/end-to-end-trust-loop.test.tsx
- job-tracker-ui/src/components/JobDetailsDialog.tsx
- job-tracker-ui/src/components/Correspondence.tsx
- .gsd/milestones/M001/slices/S05/S05-UAT.md

job-tracker-ui/src/components/Correspondence.tsx

@@ -405,6 +405,28 @@ export default function Correspondence({ jobId, job }: { jobId: number; job: Job
         )}
       </Paper>
 
+      <Box sx={{ mt: 1.5, p: 1.5, borderRadius: 3, border: "1px solid", borderColor: "divider", backgroundColor: "background.default" }}>
+        <Typography variant="overline">Linked Gmail thread continuity</Typography>
+        <Typography variant="body2" sx={{ color: "text.secondary", mb: 1.25 }}>
+          Linked Gmail refresh only checks threads that are already tied to this job, so new correspondence can appear here without re-importing the whole thread.
+        </Typography>
+        <Box sx={{ display: "flex", gap: 1, flexWrap: "wrap" }}>
+          <Chip size="small" color={gmailStatus?.connected ? "success" : "default"} variant="outlined" label={gmailStatus?.connected ? "Gmail connected" : "Gmail not connected"} />
+          <Chip size="small" color={linkedThreadIds.length > 0 ? "success" : "default"} variant="outlined" label={linkedThreadIds.length > 0 ? `Linked threads: ${linkedThreadIds.length}` : "No linked threads yet"} />
+          {linkedThreadRefresh ? (
+            <Chip
+              size="small"
+              variant="outlined"
+              label={linkedThreadRefresh.imported > 0
+                ? `Last linked refresh imported ${linkedThreadRefresh.imported} new message${linkedThreadRefresh.imported === 1 ? "" : "s"}`
+                : linkedThreadRefresh.hasLinkedThreads
+                  ? `Last linked refresh checked ${linkedThreadRefresh.threadsChecked} linked thread${linkedThreadRefresh.threadsChecked === 1 ? "" : "s"}`
+                  : "No linked Gmail refresh history yet"}
+            />
+          ) : null}
+        </Box>
+      </Box>
+
       <Box sx={{ display: "flex", gap: 1, alignItems: "flex-start", mt: 1.5, flexWrap: "wrap" }}>
         <ToggleButtonGroup exclusive value={from} onChange={(_, v) => v && setFrom(v)} size="small">
           <ToggleButton value="Me">{t("correspondenceMe")}</ToggleButton>