Avast Secure Browser is a Chromium based browser just like most browsers come to-day.
Also firefox, Iridium, Brave, ungoogled chrome, all come as chromium-(engines)-based browsers.
Even Microsoft Edge is a chromium flaw now-a-days.
Exemptions: P2P-browser Beaker, and the old Chameleon browser.
I use to run and fancy Flock from Palo Alto labs, but that is now years long obsolete and archived.
Whenever Google Chrome extensions are allowed for original Chrome Browser,
Avast Secure Browser will also run.
You only have to be persistent and when Avast Secure Browser asks allow to install a particular extension.
I personally run Local CDN(0) to run external scripts locally to avoid tracking of sorts, Privacy Badger from EFF,
Clear URLs extension, all from Google Chrome extensions, but downloaded them manually
(first Chromium Webstore, and then dragged in separately downloaded extensions,
(not recommend this method for the run of the mill usual user),
but is such way you avoid ever to log into Google account, to avoid further Google tracking).
Enjoy your Avast Secure Browsing with your personal privacy and security extensions
polonus (Avast Secure Browser beta-tester)