Implement stable serialization and restoration for dock layouts, including auto-hidden and floating panels

- Add `persistence.rs` for stable serialization of dock layouts without runtime identifiers.
- Introduce `preview.rs` for geometry handling of dock drop previews.
- Create `sizing.rs` to manage content-aware sizing policies and constraint solving for dock panels.
- Implement `welcome.rs` to provide a welcome surface when no documents are open, featuring New and Open actions.

hcie-engine-api/tests/performance_stroke_4k.rs

@@ -25,7 +25,7 @@
 //! - Allocates ~400MB of pixel/tile/mask buffers.
 //! - Uses `std::time::Instant` for measurement; results depend on the host CPU.
 
-use hcie_engine_api::{Engine, BrushTip, BrushStyle};
+use hcie_engine_api::{BrushStyle, BrushTip, Engine};
 
 const W: u32 = 3840;
 const H: u32 = 2160;
@@ -112,18 +112,29 @@ fn benchmark_4k_stroke_on_multilayer_document() {
     let total_us = total_start.elapsed().as_micros() as f64;
 
     let avg_segment_us = segment_times.iter().sum::<f64>() / segment_times.len().max(1) as f64;
-    let avg_composite_us = composite_times.iter().sum::<f64>() / composite_times.len().max(1) as f64;
+    let avg_composite_us =
+        composite_times.iter().sum::<f64>() / composite_times.len().max(1) as f64;
     let max_segment_us = segment_times.iter().copied().fold(0.0, f64::max);
     let max_composite_us = composite_times.iter().copied().fold(0.0, f64::max);
 
     println!("\n=== 4K Multi-Layer Stroke Benchmark ===");
-    println!("Canvas: {}x{}, Layers: {}, Segments: {}", W, H, LAYERS, SEGMENTS);
+    println!(
+        "Canvas: {}x{}, Layers: {}, Segments: {}",
+        W, H, LAYERS, SEGMENTS
+    );
     println!("Average stroke_to:      {:>8.1} us", avg_segment_us);
     println!("Max stroke_to:          {:>8.1} us", max_segment_us);
     println!("Average composite:      {:>8.1} us", avg_composite_us);
     println!("Max composite:          {:>8.1} us", max_composite_us);
-    println!("Total wall time:          {:>8.1} us ({:.2} s)", total_us, total_us / 1_000_000.0);
-    println!("Segments per second:    {:>8.1}", SEGMENTS as f64 / (total_us / 1_000_000.0));
+    println!(
+        "Total wall time:          {:>8.1} us ({:.2} s)",
+        total_us,
+        total_us / 1_000_000.0
+    );
+    println!(
+        "Segments per second:    {:>8.1}",
+        SEGMENTS as f64 / (total_us / 1_000_000.0)
+    );
 
     // Soft sanity check: the engine must still report a valid top layer and the
     // document must be marked modified after painting.