The author was able to confirm (see https://arunmozhi.in/2021/12/06/goodbye-brave/comment-page-1...) that they had been using version 1.18.77 of Brave (released nearly one year ago in December of 2020). This version of Brave did not contain service-keys for authentication with the proxy-server which shields users from unintended contact with Google. As a result, when Brave began to enforce key-requirements for requests (a recent change), this out-of-date build of Brave could no longer install extensions (since it could not utilize the proxy service).

Many thanks to the author for diligently assisting with this investigation.

Sampson (Brave Team)