feat(lobby): mark the real last-played game on the lobby

[netqo]

Summary

Wires the lobby's existing LAST PLAYED card design to real data: the badge now sits on the game the user actually played last, instead of the static preview default.

Rationale

The GameCard already renders the LAST PLAYED badge + highlight from a isLastPlayed flag; it was just driven by static preview data (pinned to Crash). The new LobbyViewModel reads the Room-backed game_round ledger (newest first) and exposes the most recent round's game; the lobby nav entry maps it onto the games grid (isLastPlayed = card.key == lastPlayed). No round played yet -> no card marked.

Verification

• ./gradlew testDebugUnitTest detekt ktlintCheck assembleDebug compileDebugAndroidTestKotlin green locally (JDK 17).
• New test: LobbyViewModelTest (last played is the most recent round's game; null with no rounds).
• Installed on a physical device: after playing Blackjack, the LAST PLAYED badge moved from the static Crash card to Blackjack.

Test plan

• After playing a game, its lobby card shows the LAST PLAYED badge.
• A fresh account (no rounds) marks no card.

Checklist

• Commit messages follow Conventional Commits (see CONTRIBUTING.md).
• Branch name follows the naming convention (feat/, fix/, chore/, etc.).
• The change is scoped: no unrelated edits sneaked into this PR.
• If user-visible behavior changed, CHANGELOG.md has been updated under [Unreleased].
• If a new dependency was added, it is justified in the PR description. (No new dependencies.)