I'm not really sure whether durable functions are meant to be used as a 'server'. Durable functions are part of 'serverless' and therefore I'm not sure whether it's possible (in a clean way).
To my knowledge durable functions are used to orchestrate long lasting processes. So for example handling the orchestration of a batch job. Using durable functions it's possible to create an 'Async HTTP API', to check upon the status of the processing a batch of items (durable function documentation). I've wrote a blogpost about durable functions, feel free to read it (https://www.luminis.eu/blog/azure-functions-for-your-long-lasting-logic/).
But as for your use case; I think you can create two separate Azure functions. One for posting your data, you can use an Azure Blob Storage output binding. Your second function can have a GET http trigger and depending on your data you can use an blob input binding. No need to use durable functions for it :)!
Not really a direct answer to your question, but hopefully a solution to your problem!