It may be hard to pinpoint the issue based on the limited information provided. It may be that the tutorial is outdated or the JSON payload is incorrectly formatted. The issue might also be that you are using basic logs. This is a new feature and possibly the API does not yet work with basic logs. You might try using a standard table. The cost difference is insignificant for small tables.
There is a packaged version available in Logic Apps that might be easier to use.
https://learn.microsoft.com/en-us/connectors/azureloganalyticsdatacollector/