@Tim McTa
You cannot resolve DNS queries from P2S using Private DNS Zones. Here is the link for upvoting this feature.
In this case, It's possible to make a DNS forwarder that forwards queries to Azure (virtual IP 168.63.129.16) from on-premise DNS to an azure private DNS Zone. See Name resolution that uses your own DNS server.
Please refer to this stackoverflow issue for more details. Hope this helps.
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