Remove/Hide icon for Save group in vertical view mode

[MadhaviSeelam]

Description

Found while testing #35202.

Steps to Reproduce

1. Install 1.65.89
2. launch Brave
3. opened few tabs
4. enable vertical view
5. open context menu of a tab and add tab to a new group
6. open context menu of a group
7. enable Save group

Actual result:

Save group icon is shown

Expected result:

Remove/Hide the icon

Reproduces how often:

Easily

Brave version (brave://version info)

Brave | 1.65.89 Chromium: 123.0.6312.58 (Official Build) beta (64-bit)
-- | --
Revision | 2975bd8d3905ed79de82dd9fa11b6e4019075dd6
OS | Windows 11 Version 23H2 (Build 22631.3296)

Version/Channel Information:

• Can you reproduce this issue with the current release? N/A
• Can you reproduce this issue with the beta channel? Yes
• Can you reproduce this issue with the nightly channel? Yes

Other Additional Information:

• Does the issue resolve itself when disabling Brave Shields?
• Does the issue resolve itself when disabling Brave Rewards?
• Is the issue reproducible on the latest version of Chrome?

Miscellaneous Information:

@rebron @zenparsing @aguscruiz
cc: @brave/qa-team

[rebron]

cc: @sangwoo108