Fix SQLite recovery and preserve provider conversation context

Persist exact provider history and archived tool results independently of
terminal scrollback, and retain them when active run checkpoints are cleared.
Keep conversation and session saving independent of automatic reopening.

Deduplicate only committed session snapshots, retry transient SQLite write
contention, and enqueue conversation updates before writer shutdown. Recover
healthy startup data independently and protect unread records by disabling
writes with a persistent warning after an incomplete restore. Retain local
transcript pane conversation links across restarts.

Add regression coverage for SQLite failures, context round trips, legacy
fallbacks, and transcript snapshots.

app/src/app_state.rs

@@ -23,7 +23,7 @@ use crate::workspace::tab_group::TabGroupId;
 use crate::workspace::view::left_panel::ToolPanelView;
 use crate::workspace::WorkspaceRegistry;
 
-#[derive(Debug, Clone, PartialEq)]
+#[derive(Debug, Clone, Default, PartialEq)]
 pub struct AppState {
     pub windows: Vec<WindowSnapshot>,
     pub active_window_index: Option<usize>,