I’ve set up a segment for a local loop which is 4.2km long. Exactly the same as you I just wanted it to record times over different months/years to see how I compared against myself so kept the segment settings to private.
It does display each loop as a separate timed run. So most times I’ve ridden my loop I’ve got 3-5 runs each with the same date but each with an individual time (2nd lap is normally the speedy one). It all pretty much works how you’d want it to.
Unfortunately it was so long ago that i set up the loop that I’ve forgotten how i went about it, but you can definitely do what you want to do, so its worth a little explore in strava.