Estimating resource utilization for one database
"SQLServer:Databases" perfmon counter will tell you Log activity.

If you can classify your connections (sql login user_a goes to database app_a, or connections from server B goes to database app_b, etc) then you can use a resource governor classifier function to assign connections to different workload groups.  After that, you can use the "SQLServer:Workload Group Stats" perfmon counter to see CPU usage.

Glenn Berry has DMV queries for CPU USage, IO Usage and Total Buffer Usage By Database.  https://www.sqlskills.com/blogs/glenn/sql-server-diagnostic-information-queries-for-january-2018/