Edit: To benefit the community, posting the summary of our offline discussion.
The issue was fixed by deactivating the plugin and installing it again.
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As I understand, you are trying to enable email communication through your WordPress WebApp on Azure App Service, but you are facing an issue where the action is being denied by the Resource Provider (RP).
To better assist you on this, could you please provide more info about the specific steps ( I understand you are referring to the blog post) you followed to enable email communication on your WordPress website? What is the exact error message you receive? ( Please share a screenshot after concealing any private details)
Having mentioned above, based on the error message you provided, it seems that there might be an issue with the RP.
Kindly ensure that Azure App Service and Azure Communication Service RPs are registered, checkout the doc section for the steps : Register resource provider
Also, just to highlight - Registering a RP configures your subscription to work with the resource provider. To register a resource provider, you must have permission to perform the /register/action operation for the resource provider. This operation is included in the Subscription Contributor and Owner roles.
Reference : Resolve errors for resource provider registration
Kindly let us know, I'll follow-up with you further.