Filed this issue for QA. Sidebar V2 is enabled by default with this PR (brave/brave-core#37252)
For implementation, #51462 is used.

With Sidebar V2, sidebar control UI and panel works independently.

When sidebar show option is On mouseover or Never,
clicking ai toolbar button only shows panel like below.

With On mouseover, sidebar control UI shows/hidden regardless of panel visible state.
When panel is visible, sidebar control UI can be visible/hidden with mouse move.

Sidebar toolbar button's behavior is also changed.
It's for pinning sidebar controll UI when On mouseover or Never.
With this two mode, clicking toolbar button makes sidebar control UI visible till click button again.
With Always, this button is hidden.

cc @rebron @brave/qa-team

Test plan

1. Requires 1.93.80 or higher (current Beta 1.93.116)
2. Note that sidebar is shown by default in Beta and Nightly channels and off by default in Release

Sidebar On State

1. When sidebar is on, there should be no sidebar button appearing on the toolbar.
2. Select Leo, Bookmarks, and Reading List buttons and ensure that selecting the button functions to open/close the corresponding side panel.
3. Check that moving the sidebar still functions by right clicking the side bar and selecting Move to the Left (and back) and also going to brave://settings/appearance

Sidebar Off State

1. Ensure that sidebar can enter off state by a) hamburger menu and selecting Off b) right click menu and selecting Never c) and brave://settings/appearance and selecting Never in the Sidebar section
2. Open Leo side panel via hamburger menu or toolbar button and ensure the sidebar does not appear.
3. Open the Bookmarks panel via hamburger menu or toolbar button (would need to be added to the toolbar) and ensure the sidebar does not appear.
4. Open the Reading List panel via hamburger menu or toolbar button (would need to be added to the toolbar) and ensure the sidebar does not appear.
5. Check the sidebar button in the toolbar opens and closes the sidebar only. Note that in 1.92.x the sidebar button will open the last used side panel with the sidebar.

Sidebar Autohide State

1. Ensure that sidebar can enter Autohide state by a) hamburger menu and selecting Autohide b) right click menu and selecting On mouseover c) and brave://settings/appearance and selecting On mouseover in the Sidebar section
2. Mouseover to the right side of the browser to make the sidebar appear. The UX behavior should match previous version in 1.92.x
3. Select Leo side panel, bookmarks panel, and reading list side panel and ensure that the sidebar autohides.
4. Move the sidebar to the left side and repeats steps 2 and 3.
5. Check the sidebar button appears in the toolbar and opens and closes the sidebar only. When off, check again that auto hide functions by mousing over to show/hide the sidebar.