'Move to other window' page is not shown sometimes when selecting from dialog

[Uni-verse]

Description

'Move to other window' page is not shown sometimes when selecting from dialog

Intermittent issue, usually happens after opening new windows and closing one of them. Related to https://github.com/brave/brave-browser/issues/38203

Steps to reproduce

Use Case 1:

1. New install
2. Set Enable multiple windows to ON in Appearance settings
3. Go back to new tab, long press on a favorite and select Open in new window
4. Expand one of the windows (get out of split view)
5. Open menu in either one of the windows and turn Enable multiple windows toggle to OFF in Appearance settings
6. Select merge windows in the dialog

Use Case 2:

1. New Install
2. Set Enable multiple windows to ON in Appearance settings.
3. Go back to new tab, long press on a favorite and select Open in new window.
4. Repeat this to open a third window.
5. Open menu and select Manage windows (3).
6. Select another window.
7. Toggle off Enable multiple windows
8. Select merge windows on dialog

Actual result

Move to other window page is not shown, only tab itself

https://github.com/brave/brave-browser/assets/17885425/c4c1c239-7127-470b-a49f-530976c36f8f

Expected result

Should show Move to other window page

Issue reproduces how often

Intermittent

Version/Channel Information:

• Can you reproduce this issue with the current Play Store version? No
• Can you reproduce this issue with the current Play Store Beta version? Yes
• Can you reproduce this issue with the current Play Store Nightly version? Yes

Device details

• Install type (ARM, x86): ARM
• Device type (Phone, Tablet, Phablet): Samsung GS 21
• Android version: 13

Brave version

1.66.105

[kjozwiak]

The above requires 1.66.113 or higher for 1.66.x verification(s) 👍

[Uni-verse]

Verified on Samsung Galaxy Tab S7 using version:

Brave   1.66.113 Chromium: 125.0.6422.76 (Official Build) (64-bit) 
Revision    b1864a9a0152d4f1631121c6b13a7426f50cf336
OS  Android 13; Build/TP1A.220624.014; 33; REL

• Ensured that Move to other window page is always shown when disabling the multi-window settings with multiple windows open and selecting merge windows from the dialog.
• Ensured that close windows button on multiple windows detected dialog is functional.
• Ensured that Enable multiple windows is disabled by default for new users.
• Ensured that dialog is not shown when disabling Enable multiple windows with single window open.
• Ensured use cases in https://github.com/brave/brave-browser/issues/38277#issue-2293336080 are working in incognito window.

Example	Example	Example