A number of PC games – where the hardware’s performance capabilities are going to change from player to player – have a “benchmark” option accessible, usually in the video settings, that does a “fly-through” of some relatively-intensive levels, and then gives FPS statistics (I think usually an average count, though come to think of it, a 95% number would be nice too). Thinking of a recent example, Cyberpunk 2077 does this. The earliest game that I recall that had some similar feature was Quake, with the timedemo command, though that wasn’t accessible outside of the console.
That doesn’t deal with testing controls, but it does deal with performance (and can hit a number of the engine’s features), so it does part of what you want.