Keyboard customization should arrive in the next Stable version of Brave, if not the next one finally, it’s been available in Nightly for a while and getting improved.
I don’t get the problem with the button, unless you are using the automatic expanding on hover, just expand the tabs and then close the tabs you need and then click the collapse button.
Nightly for example added a resize Vertical tabstrip, so now the distance can be reduced, compared to the default size, not as small as Edge allows, but at least Brave allows a complete collapsed use of VT unlike Edge.

Anyway, Brave can customize 99% of commands unlike other browsers, Opera which was the better one, still misses many commands that Brave allows you to edit, for example.
Saying that, you will be able to bind a hotkey to other ‘close’ tab options, and whatever Chromium allows will be added to the list of Shortcuts and Commands.
There is a feature in Brave called Quick Commands as well, which allows you to perform tasks in the address bar, rather than a separate bar like on Edge (ctrl+Q I think, if you want to see what I mean).
So you access Brave’s one with :>
and you type, like you do with any other URL or search engine.
That can also easily be a way to close tabs and move them and all. You do a ctrl+space and type close.
The Quick commands seem to support even more actions than any other Browser as well, even more commands than the Shortcuts as well, for example: Close unpinned tabs
, which is not in the list of shortcuts (for now at least).
Anyway, just be aware that “closing tabs to the right” means “below” in VT, but I guess it is hard to update the strings that say “to the right” when switching to the Vertical tabs, not like I care, the action is the same, just the string is from the Horizontal tabs.
Also, I requested for the collapse and expand shortcut and command to be added in a github issue, so it might be added soonish as well, since it was seen by Devs and they added tags for it and tagged other Devs and all that, so the point is that the expand and collapse of VT should be easier for keyboard people soon as well.