Dedup sweep: 8 small duplicate pairs across the backends (~330 lines), incl. a byte-identical 44-line function

[JDonaghy]

Problem

A set of small, high-confidence duplicate pairs between the two backends and between a backend and code that already exists in render.rs / Engine. Individually trivial; together ~330 production lines that are stated twice and can drift independently (see the GTK tab-bar issue in this chain for what that drift costs).

1. register_panel_accelerators — byte-identical, 44 lines ×2

src/app.rs:90-133 and src/tui_main/mod.rs:160-211: the same 14-entry table and the same loop. Move to src/render.rs and call it from both.

2. EngineAction dispatch — five copies

• src/app.rs:1488-1562 dispatch_engine_action
• src/app.rs:4748-4803 handle_menu_action
• src/tui_main/shell_app.rs:3808-3867 dispatch_post_key_action
• src/tui_main/shell_app.rs:2319-2395 inline MenuEvent::Activated arm
• src/tui_main/mod.rs:912-947 handle_action

The two TUI copies are near-identical to each other (OpenTerminal, RunInTerminal, OpenFolderDialog, OpenWorkspaceDialog, SaveWorkspaceAsDialog, OpenRecentDialog, QuitWithUnsaved).

Fix: render::apply_engine_action(engine, action, is_macro, &mut impl EngineActionHost) with four host hooks — open_terminal(cols, rows), folder_dialog, file_dialog, exit. ~150 lines.

3. Gutter action apply — identical 5-arm match

src/tui_main/mouse.rs:2624-2667 vs src/gtk/click.rs:465-509. The router (resolve_gutter_action) is already shared; only the apply is duplicated. Fix: render::apply_gutter_action. ~40 lines.

4. GTK re-implements engine dialog helpers

src/app.rs:5548-5582 show_quit_confirm and :5655-5690 show_close_tab_confirm duplicate Engine::show_quit_confirm / show_close_tab_confirm (src/core/engine/panels.rs:46-100) — same DialogButton literals. The TUI calls the engine (src/tui_main/shell_app.rs:2370, src/tui_main/mouse.rs:2252). Fix: delete GTK's copies. ~70 lines.

5. Session save

src/tui_main/mod.rs:948-972 vs src/app.rs:1446-1487 — same 20 lines plus GTK window size. Fix: Engine::save_session_state(). ~20 lines.

6. Explorer context action table

src/tui_main/mod.rs:690-738 vs src/app.rs:5497-5520 + :4869-4887 — same string → ExplorerAction mapping. ~40 lines.

7. GTK states sidebar_owner three times

src/app.rs:4812-4827 (current_active_panel_id), :2441-2449 (paint_sidebar_panel_rung), and the real render::sidebar_owner call at :5138. Collapse to the shared call.

8. TUI open-codes Engine::clear_sidebar_focus

src/tui_main/mouse.rs:2173-2181 sets 9 flags individually; Engine::clear_sidebar_focus() (src/core/engine/accessors.rs:575) is the same 9 assignments, and GTK calls it at src/app.rs:3855.

Also: the 5-line "collapse sidebar" sequence (hide_sidebar; has_focus = false; clear_sidebar_focus; session.explorer_visible = false; session.save) appears 5× in src/tui_main/shell_app.rs (:2779, :3134, :3298, :3480, :3512) and once at src/app.rs:5450. Extract one helper.

Fix

Take these in order, one commit each, so a failure is bisectable. Re-verify each pair immediately before editing — line numbers were measured at ee26268.

Acceptance

• These are behaviour-preserving refactors. Say so explicitly in the PR per CLAUDE.md's acceptance bar, and confirm existing black-box coverage exercises each path.
• Where an existing test does not cover a collapsed path (notably v0.3.2: tree-sitter upgrade, extensions UX, terminal install, F1 palette #4 quit/close-tab dialogs and v0.3.0: TUI-only binary (vcd) #2 EngineAction dispatch), add one and state that it fails if the collapse is done wrong.
• cargo test, cargo clippy -- -D warnings, cargo fmt pass.