Resolving the Welcome-back / Restore prompt (either Continue or New
game) cleared `PendingRestoredGame` and despawned the modal, but the
launch-time Home auto-show then fired the next frame and stacked
itself over the player's chosen path — clicking "New game" would deal
a fresh game AND immediately pop the mode picker on top.
`LaunchHomeShown` becomes pub so `handle_restore_prompt` can flip it
to `true` after either resolution; `M` still re-opens the picker on
demand. Headless tests already pre-set the flag to true via
`HomePlugin::headless()`, so they're unaffected.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
funman300
b7c3a4996f