I haven't seen anything yet on whether Brave will support it, though if I'm understanding correctly, they won't have a choice since they're using Chromium. Hopefully I'm misinformed.
It feels weird that I'm now grateful for how crap they are.
For example it is currently the reality in EU, that in order to use any of the native banking apps, a user has no choice but to expose themselves to privacy violations by either Google or Apple, i.e. US companies.
While at least one alternative exists, https://grapheneos.org/articles/attestation-compatibility-gu..., these alternatives are not being used in practice.
I see no way of preventing this happening on the web as well, if the Web Environment Integrity API ships.