At first, I recommend performance analysis. Do you know QA_DEBUG_PERFORMANCE option in qa-config.php? You should put the site in maintenance mode before setting this option. When this option is set, analysis results are shown at the bottom of the all pages. The key to performance analysis is finding the most time consuming process in the chain of processes. Rather than thinking about vague measures, it is more effective to think about measures with pinpoint.
And, if you are not using event log, I recommend that you stop event log plugin. This plugin accumulates records endlessly. This can degrade database performance (This may not be the cause.). Remember to empty the event log table after stopping the plugin.
If the overall performance of the database is not good, you may need to perform performance tuning with the optional setting of MySQL.
I hope your site's performance will improve.