fix: harden and de-slop the merged sidebar/chat/settings batch

Post-merge follow-ups for #2740 #2735 #2734 #2690 #2676 #2738 #2684
#2689 #2733 #2739 #2462 #2687 #2736 #2618 #2697, plus three regressions
found while reviewing them:

- ctrl/cmd+digit while typing no longer switches session tabs (#2503 was
  still open in practice: the guard only covered the mod+alt surface binding)
- Shiki template-call sanitizer now covers every bundled grammar, including
  the js/ts aliases and embedding grammars; timed-out highlight requests are
  memoized and no longer cancel unrelated in-flight requests
- settings flush on suspend uses keepalive and also fires on Capacitor
  appStateChange; keeps the selected model persisted across mode switches
- remote-only branches fetch before checkout; range helpers fail clearly
- git status invalidation now fires for runtime adapters too
- settings number inputs and select triggers size in ch so they scale with
  the interface font
- recent-activity timestamps tick from one list-level ticker
- Markdown preview find goes through the shared find_in_file keybind with
  containment, no longer counts its own bar, and debounces observer runs
- #2676 reverted; #2524 fixed by fading the sticky header's own background
  instead of overlaying the content below it
- sticky group headers in the model picker and sidebar render again
  (oc-sticky-fade-scroller class restored after 9b9d7069c)
- project switcher names are left-aligned again (wrapper lost in 26dbc2f30)
- tool card quick-open icon is always visible and opens the same line as the
  expanded card's button
- tautological tests replaced or removed; new oxlint findings fixed

packages/ui/src/components/session/sidebar/DOCUMENTATION.md

@@ -74,4 +74,4 @@ make every row observe unrelated streaming updates.
 - Empty successful lists, unresolved loads, and failed loads are separate UI states. Failed groups expose Retry and retain prior data.
 - Directory permission failures remain visible even when stale sessions are retained. Flat groups inspect every represented root/worktree directory; local Desktop may open the native picker for the exact failed directory, while other runtimes keep the ordinary Retry action.
 - Pins and folder assignments are not pruned from the first startup snapshot or from optimistic mutations. Confirmed local deletion and routed external deletion clean immediately; a later authoritative omission after an established baseline covers missed external delete events.
-- Pending-permission/question row badges fade with the same hover/menu-open rule as the date label, except on always-visible-actions rows, which reserve permanent padding and keep the badges shown (`selectRowBadgeVisibilityClass` in `sessions/sessionNodeItemUtils.ts`).
+- Pending-permission/question row badges fade with the same hover/menu-open rule as the date label, except on non-VS Code always-visible-actions rows, which reserve permanent padding and keep the badges shown. VS Code hover-reveals its actions over the row's right edge even under `alwaysShowActions`, so its badges keep fading (`selectRowBadgeVisibilityClass` in `sessions/sessionNodeItemUtils.ts`).