👐 fix: Open/Close Sidebar Button Animation UX Regression from #10521 (#10694)

Problem:
--------
Commit 5ed1f2991 introduced a layout shift regression when opening the
sidebar. The UI would visibly "jump" as elements shifted right before
the animation completed. Closing the sidebar worked correctly.

Root Cause Analysis:
--------------------
The accessibility PR added a redundant `{navVisible && ...}` conditional
wrapper around the `<nav>` content inside Nav.tsx's `motion.div`. This
caused a race condition:

1. User clicks "Open Sidebar" button
2. `navVisible` state becomes `true`
3. React renders the `motion.div` AND its children simultaneously
4. The inner `{navVisible && (<nav>...)}` renders content at full width
   (320px/260px) BEFORE framer-motion applies `initial={{ width: 0 }}`
5. Brief flash of full-width content causes visible layout shift
6. Animation then starts from width: 0, but damage is done

The ref-based focus management (passing `openSidebarRef`/`closeSidebarRef`
through context) was suspected but was not the actual cause. However,
`requestAnimationFrame` focus calls during animation start could trigger
forced layout calculations, exacerbating the issue.

Solution:
---------
1. Remove redundant conditional rendering in Nav.tsx
   - The outer `{navVisible && (<motion.div>...)}` already controls
     visibility
   - The `overflow-x-hidden` class on motion.div clips content during
     animation
   - Content should always exist inside motion.div for smooth clipping

2. Replace ref-based focus with ID-based focus management
   - Refs passed through component tree can affect React's reconciliation
   - Using `document.getElementById()` decouples focus from render cycle
   - Exported `CLOSE_SIDEBAR_ID` and `OPEN_SIDEBAR_ID` constants for
     consistency

3. Delay focus until after animation completes
   - Changed from `requestAnimationFrame` to `setTimeout(..., 250)`
   - Animation duration is 200ms; 250ms ensures completion
   - Prevents layout thrashing during animation

4. Clean up prop drilling
   - Removed `openSidebarRef`/`closeSidebarRef` from Root.tsx context
   - Simplified Nav.tsx, Header.tsx, NewChat.tsx prop signatures
   - Updated ContextType to remove ref properties

Files Changed:
--------------
- client/src/routes/Root.tsx
- client/src/components/Nav/Nav.tsx
- client/src/components/Nav/NewChat.tsx
- client/src/components/Chat/Header.tsx
- client/src/components/Chat/Menus/OpenSidebar.tsx
- client/src/common/types.ts

Accessibility Note:
-------------------
The original inner conditional was added to prevent keyboard navigation
to hidden sidebar content for screen readers. This is still handled by:
- AnimatePresence unmounting the motion.div after exit animation
- The motion.div having width: 0 during exit (content not reachable)
- Screen readers typically skip content being animated out
- Other: removed non-existant prop from BookmarkNav

Testing:
--------
- Verified smooth animation when opening sidebar (no layout shift)
- Verified smooth animation when closing sidebar (unchanged)
- Verified focus transfers correctly between open/close buttons
- Verified keyboard navigation works as expected

client/src/components/Nav/NewChat.tsx

@@ -3,6 +3,7 @@ import { useNavigate } from 'react-router-dom';
 import { QueryKeys } from 'librechat-data-provider';
 import { useQueryClient } from '@tanstack/react-query';
 import { TooltipAnchor, NewChatIcon, MobileSidebar, Sidebar, Button } from '@librechat/client';
+import { CLOSE_SIDEBAR_ID, OPEN_SIDEBAR_ID } from '~/components/Chat/Menus/OpenSidebar';
 import { useLocalize, useNewConvo } from '~/hooks';
 import { clearMessagesCache } from '~/utils';
 import store from '~/store';
@@ -13,16 +14,12 @@ export default function NewChat({
   subHeaders,
   isSmallScreen,
   headerButtons,
-  openSidebarRef,
-  closeSidebarRef,
 }: {
   index?: number;
   toggleNav: () => void;
   isSmallScreen?: boolean;
   subHeaders?: React.ReactNode;
   headerButtons?: React.ReactNode;
-  openSidebarRef?: React.RefObject<HTMLButtonElement>;
-  closeSidebarRef?: React.RefObject<HTMLButtonElement>;
 }) {
   const queryClient = useQueryClient();
   /** Note: this component needs an explicit index passed if using more than one */
@@ -33,10 +30,11 @@ export default function NewChat({
 
   const handleToggleNav = useCallback(() => {
     toggleNav();
-    requestAnimationFrame(() => {
-      openSidebarRef?.current?.focus();
-    });
-  }, [toggleNav, openSidebarRef]);
+    // Delay focus until after the sidebar animation completes (200ms)
+    setTimeout(() => {
+      document.getElementById(OPEN_SIDEBAR_ID)?.focus();
+    }, 250);
+  }, [toggleNav]);
 
   const clickHandler: React.MouseEventHandler<HTMLButtonElement> = useCallback(
     (e) => {
@@ -62,7 +60,7 @@ export default function NewChat({
           description={localize('com_nav_close_sidebar')}
           render={
             <Button
-              ref={closeSidebarRef}
+              id={CLOSE_SIDEBAR_ID}
               size="icon"
               variant="outline"
               data-testid="close-sidebar-button"