Removed deprecated BrowserTabsTray in 53.0.0

[jonalmeida]

In #7079, we decoupled the adapter from the BrowserTabsTray, we should be able to remove it since it doesn't provide any use for us (we can always re-add it back with a better API if we find a better use case).

When removing this, we should also move the TabsTrayStyling be a constructor param.

┆Issue is synchronized with this Jira Task

[jonalmeida]

We've removed all references to first-party browsers, we can remove BrowserTabsTray in the next release.