feat(picker): add the speedrun mood and the speedrun.com link

"What to play next" gets a Speedrun mood. The game detail links the
game's speedrun.com page when Core found one with verified runs; only
https://www.speedrun.com/ links are shown.

src/pages/PlayNextPage.test.jsx

@@ -110,6 +110,30 @@ describe('PlayNextPage', () => {
         expect(screen.getByText('PLAY_NEXT.MOOD_HINT')).toBeTruthy();
     });
 
+    it('asks for speedrun games and explains the background check', async () => {
+        mockBackend([[game(1)], []]);
+        renderPage();
+        await screen.findByText('Game 1');
+
+        fireEvent.click(screen.getByRole('button', {name: 'PLAY_NEXT.MOOD.SPEEDRUN'}));
+
+        expect(await screen.findByText('PLAY_NEXT.EMPTY_SPEEDRUN')).toBeTruthy();
+        expect(pickerUrls()[1].get('mood')).toBe('SPEEDRUN');
+        expect(screen.getByText('PLAY_NEXT.MOOD_HINT_SPEEDRUN')).toBeTruthy();
+    });
+
+    it('with a length limit, an empty speedrun pick says to change the length', async () => {
+        mockBackend([[game(1)], [game(2)], []]);
+        renderPage();
+        await screen.findByText('Game 1');
+        fireEvent.click(screen.getByRole('button', {name: 'PLAY_NEXT.BUDGET.SHORT'}));
+        await screen.findByText('Game 2');
+
+        fireEvent.click(screen.getByRole('button', {name: 'PLAY_NEXT.MOOD.SPEEDRUN'}));
+
+        expect(await screen.findByText('PLAY_NEXT.EMPTY_MOOD')).toBeTruthy();
+    });
+
     it('drops the old picks when a new budget fails to load', async () => {
         mockBackend([[game(1)]]);
         const pickerFetch = globalThis.fetch;