feat(mentor): round-level auto-fill toolbar on Projects tab (§C)

Adds an 'Auto-fill remaining' button above ProjectStatesTable on the
MENTORING round Projects tab. Calls mentor.autoAssignBulkForRound,
respecting the round's configJson.eligibility:
  - requested_only / all_advancing: enabled, count from new
    round.getProjectsNeedingMentor query
  - admin_selected: disabled with explanatory copy

Plan: docs/superpowers/plans/2026-04-28-pr4-mentor-assignment-ux.md

src/app/(admin)/admin/rounds/[roundId]/page.tsx

@@ -145,6 +145,73 @@ const stateColors: Record<string, string> = Object.fromEntries(
   Object.entries(projectStateConfig).map(([k, v]) => [k, v.bg])
 )
 
+// ═══════════════════════════════════════════════════════════════════════════
+// Mentoring round: Auto-fill remaining toolbar (Projects tab)
+// ═══════════════════════════════════════════════════════════════════════════
+
+function MentoringBulkAssignToolbar({
+  roundId,
+  configJson,
+}: {
+  roundId: string
+  configJson: Record<string, unknown>
+}) {
+  const utils = trpc.useUtils()
+  const eligibility = (configJson.eligibility as string) ?? 'requested_only'
+  const isAdminSelected = eligibility === 'admin_selected'
+
+  const { data: pending } = trpc.round.getProjectsNeedingMentor.useQuery(
+    { roundId },
+    { enabled: !isAdminSelected, refetchInterval: 30_000 },
+  )
+  const count = pending?.count ?? 0
+
+  const bulk = trpc.mentor.autoAssignBulkForRound.useMutation({
+    onSuccess: (result) => {
+      toast.success(result.message)
+      utils.round.getProjectsNeedingMentor.invalidate({ roundId })
+      utils.project.list.invalidate()
+    },
+    onError: (err) => toast.error(err.message),
+  })
+
+  const eligibilityLabel = eligibility.replace('_', ' ')
+
+  return (
+    <div className="flex items-center justify-between rounded-md border bg-muted/30 px-4 py-2.5">
+      <div className="text-sm">
+        {isAdminSelected ? (
+          <>
+            <span className="font-medium">Eligibility: admin-selected</span>
+            <span className="text-muted-foreground ml-2">
+              — auto-fill is disabled. Assign each project manually.
+            </span>
+          </>
+        ) : count > 0 ? (
+          <>
+            <span className="font-medium">{count}</span>{' '}
+            <span className="text-muted-foreground">
+              project{count === 1 ? '' : 's'} eligible for auto-fill ({eligibilityLabel})
+            </span>
+          </>
+        ) : (
+          <span className="text-muted-foreground">
+            All eligible projects have a mentor.
+          </span>
+        )}
+      </div>
+      <Button
+        size="sm"
+        onClick={() => bulk.mutate({ roundId })}
+        disabled={isAdminSelected || count === 0 || bulk.isPending}
+      >
+        {bulk.isPending ? <Loader2 className="mr-2 h-4 w-4 animate-spin" /> : null}
+        Auto-fill remaining
+      </Button>
+    </div>
+  )
+}
+
 // ═══════════════════════════════════════════════════════════════════════════
 // Main Page Component
 // ═══════════════════════════════════════════════════════════════════════════
@@ -1477,6 +1544,9 @@ export default function RoundDetailPage() {
 
         {/* ═══════════ PROJECTS TAB ═══════════ */}
         <TabsContent value="projects" className="space-y-4">
+          {isMentoring && (
+            <MentoringBulkAssignToolbar roundId={roundId} configJson={config} />
+          )}
           <ProjectStatesTable
             competitionId={competitionId}
             roundId={roundId}