You don't need to do anything wild to stop using Chrome on your Android phone! I have a stock ROM too, and I've got plenty of options for more private Chrome (and Firefox!) forks. Depending on what you use on your desktop, there's probably an equally private equivalent for your phone.
- Desktop Firefox? Mobile Firefox. With bookmark sync.
- Desktop Waterfox? Mobile Waterfox! Or Fennec or IronFox for something more private.
- Desktop Brave? Mobile Brave.
- Desktop Chromium? Cromite is great. It even has a little ad blocking now.