feat(mentor): bulk assignment + coalesced emails + team intros on round open

Round-page bulk-assign UI
- Checkboxes on every project row, header select-all, primary-tinted action
  toolbar that appears when 1+ rows are selected with an "Assign mentor…"
  CTA and Clear. Dialog lists the mentor pool with search (name/email/
  country/expertise), load indicator, and a radio picker.
- Always-visible tip strip when nothing is selected explains the bulk flow
  and offers a one-click "Select all N without a mentor" shortcut.
- New tRPC procedure `mentor.bulkAssign({ mentorId, projectIds })` assigns
  one mentor to many projects in a transaction; idempotent on the per-pair
  `(projectId, mentorId)` unique; per-project in-app notifications still
  fire for each team.
- Mutation invalidates listMentoringProjects, getProjectsNeedingMentor,
  getMentoringImportCandidates, getMentorPool, getRoundStats, project.list
  so the page reflects the new state without a refresh.

Coalesced mentor emails
- New `sendMentorBulkAssignmentEmail` (single email listing every newly-
  assigned project + workspace links) used by `mentor.bulkAssign` and
  `mentor.autoAssignBulkForRound`. The previously-silent auto-fill flow
  now emails mentors at the end of the batch, one combined email per
  mentor regardless of how many projects they received.

Team introduction emails when the round opens
- New `sendTeamMentorIntroductionEmail` lists every assigned mentor with
  name + email and a link to the workspace, so teams can reach out
  directly.
- `activateRound` (round-engine) fires the introduction for every project
  in a MENTORING round that has active mentors when the round opens.
- `mentor.assign`, `mentor.bulkAssign`, and `autoAssignBulkForRound` also
  fire the introduction immediately when the project's MENTORING round is
  already ROUND_ACTIVE — so mentors added mid-round still reach the team.
- Idempotency via the new `MentorAssignment.teamIntroducedAt` column
  (migration 20260526114936) — independent from `notificationSentAt` so
  pre-existing mentor-side stamps don't suppress the team-side email.

src/server/routers/round.ts

@@ -266,6 +266,55 @@ export const roundRouter = router({
       return { count, eligibleTotal, mentorPoolSize }
     }),
 
+  /**
+   * For a MENTORING round, find the immediately-prior round in the same
+   * competition and report how many of its PASSED projects are not yet
+   * present in this round. Drives the "Import from prior round" CTA so
+   * admins don't have to manually pick projects via the From-Round modal.
+   */
+  getMentoringImportCandidates: 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, competitionId: true, sortOrder: true },
+      })
+      if (round.roundType !== 'MENTORING') {
+        return { priorRound: null, pendingCount: 0 }
+      }
+      const prior = await ctx.prisma.round.findFirst({
+        where: {
+          competitionId: round.competitionId,
+          sortOrder: { lt: round.sortOrder },
+        },
+        orderBy: { sortOrder: 'desc' },
+        select: { id: true, name: true, status: true },
+      })
+      if (!prior) return { priorRound: null, pendingCount: 0 }
+      if (prior.status !== 'ROUND_ACTIVE' && prior.status !== 'ROUND_CLOSED') {
+        return {
+          priorRound: { id: prior.id, name: prior.name, status: prior.status },
+          pendingCount: 0,
+        }
+      }
+      const existingInTarget = await ctx.prisma.projectRoundState.findMany({
+        where: { roundId: input.roundId },
+        select: { projectId: true },
+      })
+      const existingIds = new Set(existingInTarget.map((s) => s.projectId))
+      const passedInPrior = await ctx.prisma.projectRoundState.findMany({
+        where: { roundId: prior.id, state: 'PASSED' },
+        select: { projectId: true },
+      })
+      const pendingCount = passedInPrior.filter(
+        (s) => !existingIds.has(s.projectId),
+      ).length
+      return {
+        priorRound: { id: prior.id, name: prior.name, status: prior.status },
+        pendingCount,
+      }
+    }),
+
   /**
    * List projects in a MENTORING round with their (multi-)mentor assignments.
    * Drives the per-team assignment table on the round Projects tab so admins