@OP: It all comes down to where you want to find any problems. NONE of the testing is a requirement - unless your bid document makes it so. That being said, there are certain test criteria that are strongly recommended to enhance both safety and performance.
Personally - 1) do the factory acceptance testing of individual components (motors, generators, compressors, pumps, etc.). Follow up with 2) perform no-load string testing for major (or critical) processes, usually at the driven-load supplier's facility. For really critical stuff, add in 3) a loaded string test where possible. And finally, 4) actual loaded string testing as part of the on-site commissioning process.
Why do 4) if you've already passed 3)? Because the situation at site is a combination of a lot of things beyond your immediate control - and 3) was based on what SHOULD be happening at site, not what is ACTUALLY happening.
Converting energy to motion for more than half a century