Tab group management button location improvements

Description of the issue:
Tab group management button location improvements

How can this issue be reproduced?

  1. configure vertical tab bar
  2. allow to show scrollbar on that
  3. turn on showing created and saved tab groups on bookmark bar
  4. unable to show only tab groups button on bookmark bar without tab group names
  5. while opening vertical sidebar, no tab group management buttons visible on top of sidebar

Expected result:

  1. Possible to show tab groups button only without tab group names
  2. tab group management buttons are visible on top of sidebar while opening vertical sidebar either manually or with mouse over

Here is proposal, how tab group management button and also new tab button could be visible on vertical tab bar:
image
Currently that space is empty but could be inhabited with useful buttons to improve Brave usability.

Brave Version( check About Brave):
Version 1.74.48, Chromium: 132.0.6834.83 (64-bit)

Additional Information:
Using Linux but this applies also other desktop operating systems.
When you have a bit more tab groups or their names are a bit longer, they occupy bookmark bar. When to turn off showing saved bookmark groups, also managing button disappears and no way to create new tab groups without that. Yes, we can manually remove each group from bookmark bar but this again requires manual intervention in case of every tab group. Certainly also this feature is useful but much faster would be just disable showing tab groups on bookmark bar but still show the management button.