Brave is Chromium-based and will also suffer from the Manifest v3 change. They're just activating the extended enterprise support to delay the inevitable. So no, Brave will not keep those extensions alive.
With that said, Brave's built-in ad blocker should not be affected by the change.
I don't know if this really counters my point, mainly because the tweet this is in reply to was deleted, so there might be more useful context there.
I don't have the link handy since I'm on mobile, but they've stated in a GitHub issue that they're not going to maintain v2 support, just activate the extended enterprise support to give users more runway. This just seems to be a mock-up of a toggle for that extended enterprise support and links to the extensions since they won't be downloadable from the consumer Chrome extension store.
I will admit that they haven't been clear (perhaps intentionally), but I have yet to see an announcement that explicitly states that they will independently maintain v2 support.
I assume Brave will continue to rely on Google's app store for extensions. When Manifest v2 stops being supported, aren't v2-based extensions going to fade away?
It's more of a branch than an actual fork. It's using an automated build process where they add/tweak/enable/disable stuff on top.
The analogy I like to use is they (Chromium-based browsers) are in another lane on the same road whereas a complete fork diverges to their own road. The former is still beholden to whatever direction the Chrome road goes.
Yeah, at some point Google may just straight up remove the Manifest v2 code from Chromium rather than just disable it. At that point it can get harder for Brave. Happened to them with eg. mobile slideshow tabs. Google disabled it, Brave kept the feature alive until Google removed it from the codebase.
I'm not familiar with Brave development, but I assumed they are mostly using the off-the-shelf upstream engine and putting their own browser (chrome, UX, etc.) around it.
With that said, Brave's built-in ad blocker should not be affected by the change.