feat(menu): direct SUPER+CTRL+I / SUPER+CTRL+T binds for System and Tools

BACKLOG #107: both submenus get conflict-free direct bindings through
the canonical keybinds.nix (single source for Hyprland binds and the
SUPER+? cheatsheet) — I follows the Super+I settings muscle memory,
T is Tools. The root-menu rows now show the shortcuts via menuHint.

Verified: V2 — eval audit: 41 binds, no duplicate mods+key; both binds
present in the generated Hyprland config; built nomarchy-menu passes
bash -n with cheatsheet rows + hints rendered. In-session on the live
ISO KVM run: viewed 40-system-menu.png / 41-tools-menu.png in
/tmp/nomarchy-v2-swap-93/ — each bind opens its submenu directly.
V0 flake check green.

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

agent/BACKLOG.md

@@ -109,12 +109,6 @@ guard covering every internal leaf; external GUIs and free-text prompts retain
 their explicit Esc exceptions. Pass = no internal leaf can strand the user and
 the guard fails on a regression.
 
-### 107. Direct keybindings for System and Tools menus
-
-Add conflict-free direct bindings for System and Tools through the canonical
-`keybinds.nix` source of truth. Pass = both routes open directly, generated
-Hyprland bindings and the cheatsheet agree, and conflict checks stay green.
-
 ### 108. Keybindings menu presentation and completeness audit
 
 Group the menu as Window, Workspace, Menu, and Media, then prove every live

agent/JOURNAL.md

@@ -19,6 +19,20 @@ Template:
 
 ---
 
+## 2026-07-13 — #107 direct System/Tools menu keybinds (this commit)
+- **Task:** BACKLOG #107 — conflict-free direct bindings via keybinds.nix.
+- **Did:** `SUPER+CTRL+I` → `nomarchy-menu system` (Super+I settings muscle
+  memory), `SUPER+CTRL+T` → `nomarchy-menu tools` in keybinds.nix (single
+  source: Hyprland + cheatsheet); root-menu Tools/System rows now carry
+  `menuHint` shortcut hints.
+- **Verified:** V2 — eval: 41 binds, zero duplicate mods+key; both binds in
+  the generated Hyprland config; built nomarchy-menu bash -n green with
+  cheatsheet rows + hints rendered. In-session on the live ISO: VIEWED
+  `/tmp/nomarchy-v2-swap-93/40-system-menu.png` + `41-tools-menu.png` —
+  both submenus open directly from the binds. V0 flake check green.
+- **Pending:** nothing.
+- **Next suggestion:** #99 pending the focused doctor/theme-switch VM run.
+
 ## 2026-07-13 — #93 installer swap prompt labeled + explained (this commit)
 - **Task:** BACKLOG #93 — the swap field was a bare prefilled gum input (no
   visible section, label, or unit; the placeholder never shows once a value