Start page and document tabs

Start page (shown on launch without a file, and from the house button in the application bar):
New Design, Open, recent designs (kept in the preferences, newest first) and built-in samples,
each card with a picture rendered from the design in the background. Samples are scripts of
engine commands: the sample plate plus a sheet metal bracket, a hinge assembly with a revolute
joint, a plastic enclosure (lip, bosses, rest, snap fit), a bolted flange with a parametric
circular pattern and a vent plate with a parametric rectangular pattern (test: all build
without a failing feature).

Several open designs as tabs in the application bar: each keeps its own session (undo,
selection), camera and hidden/shown items; + and Ctrl+N open a new design, opening a file or a
sample uses a new tab unless the current design is blank, closing a tab with unsaved changes
asks Save / Don't Save / Cancel. Control channel: ui.documents and ui.home (docs/control-protocol.md).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01AS5Tn3xieewUSg3uxrMVdL

crates/ui-egui/src/control.rs

@@ -104,7 +104,24 @@ pub fn handle(app: &mut SolveApp, ctx: &egui::Context, req: &ControlRequest) ->
             "frame_ms": app.frame_ms,
             "build_ms": app.viewport.build_ms,
             "preview": {"active": app.preview.active, "busy": app.preview.busy, "error": app.preview.error, "ms": app.preview.ms, "replaced": app.preview.replaced},
+            "home": app.home.open,
+            "documents": app.docs.count(),
         })),
+        "ui.documents" => ok(crate::documents::control(app, p)),
+        "ui.home" => {
+            match p.get("open").and_then(Value::as_bool) {
+                Some(true) => {
+                    let rev = app.session.revision;
+                    app.home.show(rev);
+                }
+                Some(false) => app.home.open = false,
+                None => {}
+            }
+            if let Some(i) = p.get("sample").and_then(Value::as_u64) {
+                crate::home::open_sample(app, i as usize);
+            }
+            ok(json!({"open": app.home.open, "recent": app.home.recent}))
+        }
         "ui.set" => {
             let mut cur = serde_json::to_value(&app.ui).unwrap_or(json!({}));
             if let (Some(o), Some(src)) = (cur.as_object_mut(), p.as_object()) {