As mentioned in the below post, SQL Monitor will keep serverless Azure SQL databases from pausing and saving us the money they are supposed to. I would like the Azure SQL monitoring piece to be rewritten to use the Azure API to determine both if the Azure SQL DB is serverless or not and if it is AND paused, don't run any queries that would wake it. Yet if it is NOT paused, get info about it and update SQL Monitor.

https://sqlmonitor.uservoice.com/forums/91743-suggestions/suggestions/45670060-exclude-serverless-databases-from-monitoring