test(e2e): manage games through the rebuilt Games page (LAZ-1413)

[chnexusmods]

Fixes the shared manageGame E2E helper for the rebuilt Games page. A full local run on master had 30 of its 32 failures in this helper, before any spec's own steps ran. That covers every spec that needs a managed game: Health Check, mods, Profiles, QA-103 and QA-106.

Linear: LAZ-1413

Why it broke

• "Manual add" found the wrong tile. Each tile's button now depends on its section: "Add game" under detected games, "Manual add" under all supported games, "Open" under added games. The locator searched the whole page. In logged-in tests, a game installed through a store (here Stardew Valley via Steam) is also listed under "New games detected". That section comes from a Nexus API lookup added in fe655f5, so the first match was the "Add game" tile.
• Adding a game no longer opens it. Since c755a5c (LAZ-880), the spine follows the open page. The game still becomes active, but the user stays on the Games page in Home, so the helper's wait for "Mods" never passed.

Changes

• selectors/games.ts: manualAddButton only looks under "All supported games". New openButton for "Added games". detectedSection matches both "Games detected" and "New games detected".
• helpers/games.ts: after the dialog, open the game from its tile under "Added games", then wait for Mods. manageGame is split into addGameManually and openAddedGame.
• helpers/timeouts.ts: new Timeouts.GAME_ACTIVATION for the activation waits, which aren't network-bound.

Detection gives Vortex no game path (VORTEX_E2E=1 still disables discovery), so the tests still go through the "Game not discovered" dialog and manage the fake install. They never touch a real one.

Testing

All runs local, headless, CI=1:

• Health Check and mods specs: 30/30 passed.
• game-management.spec.ts and profile.spec.ts: 5/5 passed before the helper split.
• After the split: 4/5 passed. QA-103 failed on the Nexus login captcha during test setup, before reaching this code, and needs a re-run.

Open question

Is staying on the Games page after adding a game the intended UX after LAZ-880? If not, the product change would make the extra Open step unnecessary.

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