An Azure service that provides global content delivery and acceleration.
Hi Aleksey,
First, to get past current error you are seeing you can create Ruleset with rule that puts in x-ms-version request header (this header is required for authenticated requests to storage api), similar to below screenshot:
Above Ruleset needs to be associated to your route.
Second, using Private link with Origin authentication is currently not supported. If you want to use Origin authentication as you describe then you would need to set your storage account to Enabled from all networks.
If you used storage account with long random name as your origin you would at least have "security through obscurity". Unauthenticated requests would fail (assuming you don't enable anonymous) even with public access allowed.
Screenshot from origin auth documentation page:
I'm unsure how you were able to get Azure Front Door private link enabled with Origin auth since times I've tried it an error is shown. Perhaps you didn't use portal?
Please click Accept Answer and upvote if the above was helpful.
Thanks.
-TP