My advise: Don’t think as AdGuard like an DNS blocking service. It’s not designed to work like this. DNS blocking is pretty easy to work around - since it’s not some Deep Inspection Magic
To exclude an device on the second router you have to do either:
Replicate the AdGuard configuration to the 2nd router and use an public DNS server as the root server. So you exclude the whole router.
Forward all DNS to the 1st router and exclude your chromebook there.
Oh, and of course it will only work when you use the „AdGuard handle clients directly“ switch.
Adguard is a VPN and runs internally on 127.0.0.1.
You cannot bypass adguard for specific devices etc because of the way it works by encapsulating all of the traffic.
You will have to do as said by having the adguard device doing the adguard things and those you don’t want protected on another router BEFORE that one. Isp>(not adguard router)>adguard router.