All Activity Log plugins are going to cause website performance issues due to the way the activities are captured, which is to capture DB Queries. There simply is no other way to capture activity without involving your WP database. DB Queries are the #1 most costly performance hits for a WordPress site.
I considered adding an Activity Log in BPS Pro, but decided against it due to causing website performance problems/slowness. The only way I would consider adding this type of feature would be to limit captured actions/queries to only important events/queries.
So if there is an existing Activity Log plugin that allows you to choose which activities to monitor/log then that is going to be the best Activity Log plugin. You would choose to only monitor/log important activities and not all activities/db queries.
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