So Brave would fail when Windows says, "hm, your hash doesn't match any recent Edge version, so you don't get to issue a key signing request to the TPM."
Or it will allow the request but when it arrives at the server as "Windows, non-Edge browser" they'll hit you with the endless CAPTCHAs or just boot you out as a hacker.
It's not the web I grew up in.
It seems to me like you can only guarantee no tampering in an actually locked down system, like modern mobile devices.