The return type of an async method must be void, Task or Task<T>

Change the return type to Task<Dictionary<string, float>>:

public async Task<Dictionary<string, float>> GetLikelihoodsAsync(List<string> inputs)

you can also replace your usage of ContinueWith to use await:

var response = await GetResponseAsync(requestData, client, uri);
var result = await ParseResponseAsync(response);
return result;

As stated in the error:

The return type of an async method must be void, Task or Task<T>

In your case that would be Task<T>, or specifically Task<Dictionary<string, float>>. So, your method needs to be declared as this:

public async Task<Dictionary<string, float>> GetLikelihoodsAsync(List<string> inputs)

Note that you don't actually need to return a Task<T>, you only need to return T. You can read more about it here.

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