refactor: DRY cleanup — extract shared helpers, remove duplication across tools, LSP, overlays, and runtime

Eliminate ~500 lines of duplicate code across 31 files by extracting
shared functions, helpers, and consolidating repeated patterns.

Highlights:
- Toast helpers (toast_info/success/warning/error) on AppStateRest
- push_event() helper for turn-event queue (19 callers consolidated)
- log_write_edit_tool() shared fn (turn.rs + engine.rs ~50 lines saved)
- resolve_api_key() shared fn (spawn.rs + provider.rs)
- LSP call_positional() helper on LspClient
- lsp_cursor_params() shared schema for 4 tool files
-overlay_block() helper for consistent overlay title/border styling
- cycle_selected_index(), path_not_found/a_directory() helpers
- mark_dirty(), save_settings() on AppStateRest
- Remove redundant Err(e) => Err(e) arms in LSP tools
- Consolidate generate_workspace_tree (turn.rs → workspace.rs)
- Simplify background-review wrapper args in auto/mod.rs

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

crates/zesdex-backend/src/app/state/rest.rs

@@ -347,10 +347,35 @@ impl AppStateRest {
         self.dirty = true;
     }
 
+    /// Mark the app state as dirty, triggering a TUI re-render on the next frame.
+    pub fn mark_dirty(&mut self) {
+        self.dirty = true;
+    }
+
     /// Queue a toast notification for display and mark the app dirty.
     pub fn push_toast(&mut self, toast: Toast) {
         self.misc.push_toast(toast);
-        self.dirty = true;
+        self.mark_dirty();
+    }
+
+    /// Push an info toast with the given message.
+    pub fn toast_info(&mut self, msg: impl Into<String>) {
+        self.push_toast(Toast::new(super::types::ToastKind::Info, msg.into()));
+    }
+
+    /// Push a success toast with the given message.
+    pub fn toast_success(&mut self, msg: impl Into<String>) {
+        self.push_toast(Toast::new(super::types::ToastKind::Success, msg.into()));
+    }
+
+    /// Push a warning toast with the given message.
+    pub fn toast_warning(&mut self, msg: impl Into<String>) {
+        self.push_toast(Toast::new(super::types::ToastKind::Warning, msg.into()));
+    }
+
+    /// Push an error toast with the given message.
+    pub fn toast_error(&mut self, msg: impl Into<String>) {
+        self.push_toast(Toast::new(super::types::ToastKind::Error, msg.into()));
     }
 
     /// Resolve the base directory that stores this session (grandparent of
@@ -385,6 +410,17 @@ impl AppStateRest {
             )
     }
 
+    /// Persist the current settings to the store and swallow any error.
+    ///
+    /// Inline usage of `JsonSettingsRepository::new().save(...)` was
+    /// duplicated twice in `controller/input.rs` — this helper centralises
+    /// the call site.
+    pub fn save_settings(&self) {
+        use zesdex_cms::domain::repository::SettingsRepository;
+        let _ = zesdex_cms::infrastructure::persistence::settings_repo::JsonSettingsRepository::new()
+            .save(&self.store_base_dir(), &self.settings);
+    }
+
     /// Build a `ToolCtx` for tool calls originating from the main agent.
     pub fn tool_ctx(&self) -> crate::tool::ToolCtx {
         self.tool_ctx_for(Origin::Main)