fix(ui): F8-04b lobby — auto-expand first available games sub + hide empty invitations

Two follow-up nits on the F8-04b sidebar:

1. The bare-`lobby` resolver (lobby-screen.svelte) redirected to
   `games-recruitment` unconditionally on mount. With games already
   in the player's roster the sidebar then highlighted the wrong
   sub-page. The resolver now awaits the lobby fan-out + account
   fetch, then hands off to the same `firstVisibleGamesScreen` helper
   the sidebar uses — so a fresh entry with games lands on
   `active-past`, the canonical-order fallback stays `recruitment`.

2. `games-invitations` was unconditionally visible in the sidebar.
   Now it follows the `active-past` rule: hidden until the
   pending-invites list reports >=1. The lobby shell's auto-kick
   effect treats it symmetrically — accepting / declining the last
   invite moves the player to the next visible sub-page once the
   fan-out has resolved.

Acceptance order in games-invitations-screen.acceptInvite was also
swapped to setMyGames-before-removeInvitation: both mutations land
in the same microtask, so the new auto-kick sees the freshly added
game in `myGames` when invitations drop to zero and routes the
player to `active-past` instead of bouncing through `recruitment`.

The visibility predicates and canonical order live in the new
`src/lib/lobby-nav.ts` pure helper, shared between the sidebar and
the resolver so they cannot disagree. Unit tests cover every
combination of (hasMyGames, hasInvitations, isPaidOrDev).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

ui/frontend/src/lib/lobby-nav.ts

@@ -0,0 +1,66 @@
+// Pure helpers for the lobby `games` submenu.
+//
+// Both the sidebar (`lib/screens/lobby-shell.svelte`) and the bare-`lobby`
+// resolver (`lib/screens/lobby-screen.svelte`) need to agree on which
+// sub-screen is the "first available" — the one auto-expanded in the
+// sidebar and the redirect target when the user lands on the bare lobby
+// alias. Centralising the predicates here keeps the two surfaces from
+// drifting apart.
+//
+// The functions are intentionally pure: they take a resolved snapshot of
+// lobby / account state, return the visible sub-screen list (in canonical
+// order) and the first entry, and never touch stores or globals. Callers
+// derive the state from `lobbyData` / `account` and the DEV-affordances
+// flag.
+
+export type GamesSubScreen =
+	| "games-active-past"
+	| "games-recruitment"
+	| "games-invitations"
+	| "games-private-games";
+
+/**
+ * LobbyNavState is the resolved snapshot of the lobby state the
+ * games-submenu visibility rules depend on. Build it from the live
+ * stores at the call site; the helpers below stay pure on top.
+ */
+export interface LobbyNavState {
+	/** Player has at least one own / past game in `lobby.my-games.list`. */
+	readonly hasMyGames: boolean;
+	/** Player has at least one pending invite in `lobby.invites.list`. */
+	readonly hasInvitations: boolean;
+	/** Player is on a paid tier, or the build exposes DEV affordances. */
+	readonly isPaidOrDev: boolean;
+}
+
+/**
+ * visibleGamesSubScreens returns the games-submenu sub-screens that
+ * are currently visible, in canonical display order:
+ *
+ *   1. `games-active-past` — only when the player has games.
+ *   2. `games-recruitment` — always visible.
+ *   3. `games-invitations` — only when the player has pending invites.
+ *   4. `games-private-games` — only when paid-tier or DEV.
+ *
+ * `games-recruitment` is unconditional, so the returned array is
+ * always non-empty.
+ */
+export function visibleGamesSubScreens(
+	state: LobbyNavState,
+): readonly GamesSubScreen[] {
+	const out: GamesSubScreen[] = [];
+	if (state.hasMyGames) out.push("games-active-past");
+	out.push("games-recruitment");
+	if (state.hasInvitations) out.push("games-invitations");
+	if (state.isPaidOrDev) out.push("games-private-games");
+	return out;
+}
+
+/**
+ * firstVisibleGamesScreen returns the first entry from
+ * `visibleGamesSubScreens(state)`. Since `games-recruitment` is
+ * unconditional, the result is always defined.
+ */
+export function firstVisibleGamesScreen(state: LobbyNavState): GamesSubScreen {
+	return visibleGamesSubScreens(state)[0]!;
+}