DNS doesn't quite work the same way with OpenWrt as it would on a device like a phone.
It really need to be set in dnsmasq, but this doesn't happen via the push/pull methods described.
The thread below is old and related to Wireguard, but the point is similar insofar as the DNS construct for VPNs under OpenWrt.
You can use the up/down scripts to help set/unset the desired DNS.
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