fix(start): complete Start page workflow

Track Save As paths, persist the selected section, and size tabbed
panels from their actual available width.

Refs #443

src/app/config.rs

@@ -20,6 +20,8 @@ pub struct AppConfig {
     pub settings: UserSettings,
     /// Recent-files list + retained count.
     pub recent: RecentConfig,
+    /// Last selected section on the tabbed Start page.
+    pub start: StartConfig,
     /// Which status-bar pills the user has hidden.
     pub statusbar: StatusBarConfig,
     /// Ribbon collapse density.
@@ -34,6 +36,7 @@ impl Default for AppConfig {
         Self {
             settings: UserSettings::default(),
             recent: RecentConfig::default(),
+            start: StartConfig::default(),
             statusbar: StatusBarConfig::default(),
             ribbon: RibbonConfig::default(),
             plot: PlotDialogState::default(),
@@ -59,6 +62,12 @@ impl Default for RecentConfig {
     }
 }
 
+#[derive(Clone, PartialEq, Serialize, Deserialize, Default)]
+#[serde(default)]
+pub struct StartConfig {
+    pub section: super::StartSection,
+}
+
 #[derive(Clone, PartialEq, Serialize, Deserialize, Default)]
 #[serde(default)]
 pub struct RibbonConfig {