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I'm glad that you were able to resolve your issue and thank you for posting your solution so that others experiencing the same thing can easily reference this!
Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others", I'll repost your solution in case you'd like to "Accept" the answer.
Issue :
Use OnPrem Custom DNS server for P2S Clients via transit over Azure (P2S ---- AzVPNGateway ---- S2S)
Solution :
- You changed the "Interface settings" to "Respond only on interface eth0" in the DNS section of the pi-hole.
- Post this just setting the server IP in the DNS settings of the VNET does the trick.
Kindly let us know if this helps or you need further assistance on this issue.
Thanks,
Kapil
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