moving bookmark folder from Bookmarks Toolbar to Other Bookmarks still displays on toolbar

[LaurenWags]

Test plan

#12589 (comment)

1. Open Bookmarks Manager
2. Add a folder under 'Bookmarks Toolbar'
3. Verify folder displays on the Bookmarks Toolbar.
4. Drag and drop the folder from step 2 to 'Other Bookmarks'
5. Folder should move

Description

Using the Bookmark Manager, if you move a folder from Bookmarks Toolbar to Other Bookmarks, the folder still displays on the toolbar until you add another folder.

Steps to Reproduce

1. Open Bookmarks Manager
2. Add a folder under 'Bookmarks Toolbar'
3. Verify folder displays on the Bookmarks Toolbar.
4. Drag and drop the folder from step 2 to 'Other Bookmarks'

Actual result:
Folder still displays on the Bookmarks Toolbar:

Expected result:
Bookmark Folder should not display on the Toolbar.

Reproduces how often:
Easily

Brave Version

about:brave info:
Brave | 0.20.14
V8 | 6.3.292.48
rev | 5d75826
Muon | 4.5.33

Reproducible on current live release:
No, not reproducible due to #12378

Additional Information

Found by @kjozwiak and reproduced on MacOS

[LaurenWags]

Able to reproduce with these steps (reproduced on Win by @srirambv )
Have a folder on Bookmarks Toolbar
Right click on the folder, Edit Folder
Change location to be 'Other Bookmarks' instead of 'Bookmarks Toolbar', click Done.
Folder continues to display on Bookmarks Toolbar.