feat(engine): Phase B home hierarchy — Continue card, hero New Game, deal-options disclosure

Restructures the Home overlay per docs/ui-redesign-2026-07.md Phase B:

- Continue card (mode / elapsed / score) when a game is in progress;
  clicking returns to the table
- Hero New Game replays the persisted Settings::last_mode (new field,
  serde-default Classic) with one tap; locked modes fall back to Classic
- Deal options (draw 1/3, winnable-only, difficulty tiers) move into a
  disclosure under the hero — off the Home top level (decision 2)
- Compact symmetric 2x3 mode grid; descriptions on wide viewports only
- Stats strip moves to the bottom (right pane on wide)
- Two-pane body on wide viewports (>= 1000 logical px) via new
  ui_modal::spawn_modal_sized (default card stays 720 px)
- Cancel becomes "Back to table" and only renders while a live
  (un-won) game exists

10 new home_plugin tests; all 936 engine tests + clippy green.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

solitaire_data/src/settings.rs

@@ -9,7 +9,10 @@ use std::io;
 use std::path::{Path, PathBuf};
 
 use serde::{Deserialize, Serialize};
-use solitaire_core::{DrawStockConfig, game_state::DifficultyLevel};
+use solitaire_core::{
+    DrawStockConfig,
+    game_state::{DifficultyLevel, GameMode},
+};
 
 const SETTINGS_FILE_NAME: &str = "settings.json";
 
@@ -248,6 +251,12 @@ pub struct Settings {
     /// cleanly to `None` via `#[serde(default)]`.
     #[serde(default)]
     pub last_difficulty: Option<DifficultyLevel>,
+    /// Mode of the last game the player launched from the home overlay.
+    /// The home hero "New Game" button replays this mode with one tap.
+    /// Older `settings.json` files written before this field existed
+    /// deserialize cleanly to `GameMode::Classic` via `#[serde(default)]`.
+    #[serde(default)]
+    pub last_mode: GameMode,
     /// Custom public name displayed on the leaderboard. When `None`, the
     /// player's server `username` is used instead. Trimmed to 32 characters
     /// before submission. Older `settings.json` files written before this
@@ -415,6 +424,7 @@ impl Default for Settings {
             disable_smart_default_size: false,
             replay_move_interval_secs: default_replay_move_interval_secs(),
             last_difficulty: None,
+            last_mode: GameMode::Classic,
             leaderboard_display_name: None,
             leaderboard_opted_in: false,
             take_from_foundation: true,