I ran into this same issue before when moving data from Bing Maps into Azure Maps, and the reason you can’t find an “Import JSON” button is because Azure Maps doesn’t support direct JSON uploads in the portal.
The only way to import JSON (GeoJSON) is through the Data Upload API or the Conversion API.
In practice you have two options:
If your file is GeoJSON, use the Azure Maps Data Upload API to upload it into a dataset.
If your file is a Bing Maps JSON format, first convert it to GeoJSON using the Azure Maps Conversion API, then upload it.
There is no UI-based importer in Azure Maps. Everything goes through the APIs.