Using topic client, call RegisterMessageHandler which is used to receive messages continuously from the entity. It registers a message handler and begins a new thread to receive messages. This handler is waited on every time a new message is received by the receiver.
subscriptionClient.RegisterMessageHandler(ReceiveMessagesAsync, messageHandlerOptions); References:
https://www.c-sharpcorner.com/article/azure-service-bus-topic-and-subscription-pub-sub/

Instead pass the HTTP trigger payload into an Azure Service Bus queue to be processed by a queue trigger function and return an immediate HTTP success response.
Note: Large, long-running functions can cause unexpected timeout issues. General best practices include:
Whenever possible, refactor large functions into smaller function sets that work together and return responses fast. For example, a webhook or HTTP trigger function might require an acknowledgment response within a certain time limit; it's common for webhooks to require an immediate response. You can pass the HTTP trigger payload into a queue to be processed by a queue trigger function. This approach lets you defer the actual work and return an immediate response.
Reference:
https://docs.microsoft.com/en-us/azure/azure-functions/functions-best-practices

Explanation:

Box 1: Inbound.
A set-variable policy to store the detected user identity.
Example:
<policies>
<inbound>
<!-- How you determine user identity is application dependent -->
<set-variable
name="enduserid"
value="@(context.Request.Headers.GetValueOrDefault("Authorization","").Split(' ')[1].AsJwt()?.Subject)" /> Box 2: Inbound A cache-lookup-value policy Example:
<inbound>
<base />
<cache-lookup vary-by-developer="true | false" vary-by-developer-groups="true | false" downstream-caching- type="none | private | public" must-revalidate="true | false">
<vary-by-query-parameter>parameter name</vary-by-query-parameter> <!-- optional, can repeated several times -->
</cache-lookup>
</inbound>
Box 3: Outbound
A cache-store-value policy.
Example:
<outbound>
<base />
<cache-store duration="3600" />
</outbound>
Box 4: Outbound
A find-and-replace policy to update the response body with the user profile information.
Example:
<outbound>
<!-- Update response body with user profile-->
<find-and-replace
from='"$userprofile$"'
to="@((string)context.Variables["userprofile"])" />
<base />
</outbound>
Reference:
https://docs.microsoft.com/en-us/azure/api-management/api-management-caching-policies
https://docs.microsoft.com/en-us/azure/api-management/api-management-sample-cache-by-key

Explanation: