It appears that Chrome, Firefox, and soon Edge, support the new Brotli compression algorithm over HTTPS only.
I can't find anything on whether this new compression algorithm is susceptible to the BREACH attack. The only relevant thing that I found was at the end of section 12 of RFC 7932:
A possible attack against a system that sends compressed data over an encrypted channel is the following. An attacker who can repeatedly mix arbitrary (attacker-supplied) data with secret data (passwords, cookies) and observe the length of the ciphertext can potentially reconstruct the secret data. To protect against this kind of attack, applications should not mix sensitive data with non-sensitive, potentially attacker-supplied data in the same compressed stream.
From that paragraph it appears that Brotli is still susceptible to BREACH. If my understanding of BREACH (and the related CRIME attack) is correct, compression is unsafe over HTTPS.
In this case is it safe to use Brotli for HTTPS content? If not then why are browser vendors supporting it?