This can be toggled in brave://flags on version 1.45 or later. This requires restarting the browser.

It doesn't currently support nesting (hopefully coming soon?), but you can do tab groups.

I haven't tested long enough to be able to know how stable this is, but I use the Dev build and in general it is fine.

I'm not affiliated with Brave or the dev who built the feature. I'm just a happy Brave user who has been searching for get tabbed browsing for a very long time!

1: https://github.com/brave/brave-core/pull/13816#issuecomment-1262205165