refactor: migrate search panel to SidebarSystem (#323, #333, #334) - #342

… both backends

`render::route_terminal_key` states the rung once; both backends call it and
have nothing bespoke left. `render::route_terminal_resize` does the same for
the "window resized → resize the PTYs" half.

**quadraui first (`CLAUDE.md`, and the issue's own note).** quadraui#343 has
landed on the pinned rev (`TerminalSession::paste` /
`bracketed_paste_enabled`), so the bracketed-paste rung is now an *adoption*:
`Engine::terminal_paste` delegates to it instead of wrapping unconditionally,
which stops literal `[200~` bytes leaking into programs that don't strip them.
quadraui#342 (the keyboard→PTY encoder) has **not** landed, so the encoder
stays in `core::engine::terminal_ops::key_to_pty_bytes` — platform-neutral
`core`, not per-backend code. When #342 lands, that fn is the single call site
to swap and neither backend changes.

**What diverged.** TUI hand-rolled ~75 lines inside `handle_key_pressed`. GTK's
twin was deleted outright by the #540 Relm4→ShellApp cutover — the whole
`if engine.borrow().terminal_has_focus { … }` block lived in the `view!`'s
`EventControllerKey` closure and nothing replaced it. Since #540, **every key
typed into a focused terminal on GTK fell through to `Engine::handle_key` and
ran a vim command on the editor buffer** (#471): Ctrl+F opened the editor's
find/replace overlay, `x` deleted a character from the file. The other half of
#471 was that old arm's `sender.input(Msg::Resize)` after each keypress, whose
handler resized *every* pane to the full panel width — in split mode that
reflowed the half-width panes while they were still painted narrow, so freshly
typed text in the right pane wrapped out of view. The router performs no
resize, and `route_terminal_resize` is split-aware, so neither half can return.

Also reconciled: `canonical_terminal_key_name` accepts both backends' spellings
(`PageUp`/`Page_Up`, `BackTab`/`ISO_Left_Tab`, `Enter`/`Return`) and strips the
`Shift_` prefix `translate_key` adds for the editor — which is why the old TUI
arm bypassed `translate_key` and re-derived names from the raw `KeyCode`. That
bypass is gone. The GTK rung sits directly below the focus owners and *above*
the debug F-keys, matching TUI's ladder: `vim`/`htop` inside the terminal must
get F5 themselves.

Black-box coverage, both backends, asserting on rendered output only:
- `terminal_ctrl_f_opens_the_painted_find_bar{,_via_shell_app}` — the painted
  `" FIND: …"` toolbar text (`render::build_terminal_toolbar`), then the typed
  query reaching it. Never `terminal_find_active`.
- `focused_terminal_swallows_editor_keys{_on_gtk,_via_shell_app}` — the painted
  buffer line, with a positive control (same fixture, terminal unfocused, the
  identical key must delete the character).
- `route_terminal_resize_keeps_a_split_split` — the PTYs' own `cols()`, which
  is what the painter reads back.
- `canonical_terminal_key_name_reconciles_both_backends_spellings`.

**Verified RED against unfixed `develop`** (`CLAUDE.md` rule 2): with the two
`route_terminal_key` calls and the `route_terminal_resize` body removed, all
five behaviour tests fail; restored, all pass.

Entry-point production lines (`handle_key_press` + `dispatch_gtk_panel_
accelerator` + `handle_key_pressed` + `handle_focus_owner_key` +
`dispatch_panel_accelerator_sizeless`): **1,423 → 1,389**, a strict decrease
even though GTK *gained* a rung it did not have.

`cargo build && cargo clippy -- -D warnings && cargo fmt --check` EXIT=0.

Beyond the issue's file list: `core/engine/terminal_ops.rs` (new
`Engine::terminal_paste`) and `core/engine/keys.rs` (`route_paste`'s terminal
branch now calls it) — required for the quadraui#343 adoption.

Refs #758, #734, #351, #471, quadraui#342, quadraui#343.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>