Haubein, Ted Thanks for posting your question in Microsoft Q&A. From the description above, Azure Function app is unable to connect to Oryx via VNET however, if you establish a Test VM in the same VNET, it works fine. Correct?
This appears to be due to Outbound IP restrictions and if you have Route All enabled, then all outbound traffic will be sent through Virtual Network. Then in that case you can configure NSG to allow traffic to Oryx (or other resources) and you don't need Azure Firewall. However, if Route All isn't enabled, NSGs are only applied to RFC1918 traffic. Similarly, the same case applies to route table as well. I suggest you review the docs and validate how it is configured so that you NSG (as well as route table) rules are in effect.
Also, you mentioned about DNS issues via Kudu. Do you face the issue when following the steps in https://learn.microsoft.com/en-us/azure/azure-functions/functions-networking-options?tabs=azure-cli#tools? Make sure DNS server is accessible via nameresolver
like described in Debug access to virtual network-hosted resources.
Also, validate the reasons described here and if it doesn't help, let me know. We might need to investigate the backend logs to find the cause.
If you found the answer to your question helpful, please take a moment to mark it as Yes
for others to benefit from your experience. Or simply add a comment tagging me and would be happy to answer your questions.