Hello
Application Insights
Application Insights is billed based on the volume of telemetry data that your application sends and the number of web tests that you choose to run. The telemetry data is billed per Azure Log Analytics data ingestion rates.
Log Analytics
For Azure Monitor Log Analytics, you pay for data ingestion and data retention
There are some costs if you utilize features such as alerts, or perform queries via automation solutions such as Logic Apps. But this is the cost of that using feature/ solution and not the query.
TLDR: adhoc KQL queries are non-billable as pricing is related to data ingestion / retention
https://azure.microsoft.com/en-us/pricing/details/monitor/
regards
Alistair Ross #MSFT