hello! We're having an issue where are NS instances (sandbox and production) are super slow (loading saved searches, running processes, loading records, etc). We are looking to do a "Performance Health Check" on the system in order to diagnose and resolve some of these issues. Does anyone have experience in this area and/or ideas of what this may look like?

I recommend checking out Application Performance Management (APM). It is a free SuiteApp that you can install. Also, check your Concurrency Monitor and SuiteCloud Processors Monitor. These are found under Customizations > Performance.