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/mode/mod.rs

@@ -11,3 +11,22 @@ pub mod quit_confirm;
 pub mod rewind;
 pub mod settings;
 pub mod todo;
+
+/// Cycle `current` in the range `[0, len)`.
+///
+/// * `forward = true` — increment (wrap at len)
+/// * `forward = false` — decrement (wrap at 0), saturating at 0 when len is 0
+///
+/// Return: `0` when `len == 0`, otherwise the wrapped index.
+pub fn cycle_selected_index(current: usize, len: usize, forward: bool) -> usize {
+    if len == 0 {
+        return 0;
+    }
+    if forward {
+        (current + 1) % len
+    } else if current == 0 {
+        len.saturating_sub(1)
+    } else {
+        current - 1
+    }
+}