Recent Chrome in Linux doens't allow to set search.brave.com as default search engine

Description of the issue:

Chrome 100.0.4896.88 in linux changed menus to configure default search engine. Now there is no button to add a new search engine, it only presents 6:
image

When I try to change one of the existing search engines, after I type search.brave.com it appears the message “Not Valid”:

image

This message doesn’t appear when I type other domains. So IMHO it is an unfair trick of google.

I would not use chrome in Linux but:

  1. Several google sites like drive, youtube, etc. don’t allow me to login with brave:

  2. I was using chromium but recently chromium is not saving my session in drive, youtube and other google sites, so I have to authenticate every time I close and open Chromium.

Brave Version (check About Brave):

I’m a happy user of brave, right now using 1.37.113

Operating System:

Linux.

I also use OpenBSD/adJ a lot but no support for Brave there.