Unify mobile terminal input with Composer and Direct modes

[powerfooI]

Mobile typing had separate keyboard and composer entry points with no clear indication of the active input mode. Add one bottom-right Type entry that opens a dock with a Composer / Direct switch. Composer uses native editing with separate Insert and Send actions; Direct sends keys through the terminal. Mode changes preserve the draft and caret, and a light terminal tap opens Direct input without treating scrolling or selection as typing.

Keep the configured two shortcut rows, add a show/hide toggle in the dock, and fit the floating 2x8 grid within the available width without horizontal scrolling. Group Tabs with Workspaces and Terminal/Files/Changes with the floating controls toggle, with collapse animations anchored to that toggle and a stable position on either edge. The input toolbar wraps at large interface scales so its mode control cannot overlap adjacent buttons.

Closes #286.

Validation:

• bun run build:web — passes, including existing asset budgets.
• bun run precommit — formatting, lint, types, and tests pass: 2365 passed, 2 conditionally skipped, 0 failed.
• Manual checks in the Codex in-app browser on macOS against a live Herdr backend: 320px, 360px, 390px, and 736px landscape layouts at 150% interface scale; no toolbar overlap or horizontal overflow; Composer/Direct switching preserves the draft and focus behavior. The floating grid displays all 16 slots within its panel.
• Physical iOS Safari and Android Chrome IME, keyboard, and touch-selection acceptance remains a manual device check.