feat(offline): randomise the hotseat seating (random first mover)

The 2-4 hotseat players now start in a random seating order (so who goes
first, and the turn order, is random) — matching the online games. The
engine starts at seat 0, so shuffling the seats at creation picks the
starter; the shuffle is seed-driven (a distinct derivation from the tile
bag), so replay reproduces it. Scoped to hotseat — vs_ai stays human-first.
- lib/roster.ts: shuffleSeeded (unit-tested); NewGame shuffles buildSeats
  with the game seed before create.
- e2e: pin a seed that keeps the roster order so the lock assertions stay
  deterministic.

ui/src/lib/roster.test.ts

@@ -1,5 +1,5 @@
 import { describe, expect, it } from 'vitest';
-import { buildSeats, commitName, rosterReady, type RosterRow } from './roster';
+import { buildSeats, commitName, rosterReady, shuffleSeeded, type RosterRow } from './roster';
 
 describe('commitName (keep-last-valid)', () => {
   it('commits a valid, trimmed name', () => {
@@ -48,3 +48,21 @@ describe('buildSeats', () => {
     expect(seats.every((s) => !('accountId' in s) || s.accountId === undefined)).toBe(true);
   });
 });
+
+describe('shuffleSeeded', () => {
+  it('is deterministic for the same seed', () => {
+    expect(shuffleSeeded([0, 1, 2, 3], 42n)).toEqual(shuffleSeeded([0, 1, 2, 3], 42n));
+  });
+
+  it('keeps every element (a permutation) and does not mutate the input', () => {
+    const input = [0, 1, 2, 3];
+    const out = shuffleSeeded(input, 7n);
+    expect([...out].sort((a, b) => a - b)).toEqual([0, 1, 2, 3]);
+    expect(input).toEqual([0, 1, 2, 3]); // input untouched
+  });
+
+  it('varies the order across seeds (not always the identity)', () => {
+    const orders = new Set([1n, 2n, 3n, 4n, 5n, 6n, 7n, 8n].map((s) => shuffleSeeded([0, 1, 2, 3], s).join('')));
+    expect(orders.size).toBeGreaterThan(1);
+  });
+});