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/server/routers/round.ts

@@ -215,6 +215,35 @@ export const roundRouter = router({
       )
     }),
 
+  /**
+   * Count projects in a MENTORING round eligible for mentor auto-fill
+   * (i.e., no mentorAssignment, scoped by configJson.eligibility).
+   * Used by the Auto-fill remaining toolbar on the round Projects tab.
+   */
+  getProjectsNeedingMentor: adminProcedure
+    .input(z.object({ roundId: z.string() }))
+    .query(async ({ ctx, input }) => {
+      const round = await ctx.prisma.round.findUniqueOrThrow({
+        where: { id: input.roundId },
+        select: { roundType: true, configJson: true },
+      })
+      if (round.roundType !== 'MENTORING') return { count: 0 }
+      const config = (round.configJson ?? {}) as Record<string, unknown>
+      const eligibility = (config.eligibility as string) ?? 'requested_only'
+      if (eligibility === 'admin_selected') return { count: 0 }
+
+      const count = await ctx.prisma.projectRoundState.count({
+        where: {
+          roundId: input.roundId,
+          project: {
+            mentorAssignment: null,
+            ...(eligibility === 'requested_only' ? { wantsMentorship: true } : {}),
+          },
+        },
+      })
+      return { count }
+    }),
+
   /**
    * Delete a round
    */