Frankly, I don't know if you could block ads in Chrome while using AdAway in VPN mode
A year+ ago I had two phones, rooted and not-rooted one, both with AdAway (one hosts, the other VPN mode), both running Chrome with Lite mode off.
On the rooted phone, AdAway blocked ads in Chrome and 'everwhere' (of course, not in e.g. YT).
On the not rooted phone ads were blocked 'everywhere' but I never managed to let AdAway block them in Chrome
Nowadays I have only the rooted phone and AdAway still perfectly blocks me ads in Chrome and 'elswhere'
Btw, Chrome for me is essential, primarily because of the built-in translator - sometimes, if I want I even read in Japanese, Chinese, Arabian, whatever
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If you have Android 9 or higher, disable AdAway and enable Private DNS in your native Settings, and for DNS provider put e g: dns.adguard.com
I don't recall anymore but I think Chrome will also bypass that VPN and you will still see the ads in Chrome (that Private DNS uses VPN to the configured DNS server which blocks the sites pushing ads by not resolving their DNS names)
IMHO, only some pretty old versions of Chrome can be enforced to go through your VPN (AdAway or Private DNS), and that's why you cannot block ads in Chrome, with AdAway in the non-root mode