I cant select one :)
if you insist I would actually start looking at Azure Functions first
As you said Calls to it will occur infrequently You can actually look at Azure function with Consumption plan so you only pay for what you use. But there is a Problem with a cold start which will have latency. if its the problem then go with Function with premium Plan.
Depending on you want to expose it, you can use APIM to put on top of it.
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