The Milky Way is ~100,000 light years across, and the penultimate harvest took place ~50,000 years ago. If they wanted to see what happened back then, couldn't they literally look back in time? Hypothetically, there should be many vantage points within the galaxy where the events of the first harvest would be plainly visible, or at least anomalous enough to warrant keeping space telescopes pointed in that direction. Pick a spot you know the Protheans had been, pick another spot ~50,000 light years from there, and observe.
While this might be harder with current space telescopes, unless I'm mistaken, telescopy in the setting of Mass Effect wouldn't have to be all that much better than the state of the art. We do have a tough time seeing past Pluto for example, but only because it's so dark out there. If there were some sort of explosion in the Kuiper belt, like maybe a Mass Relay short-circuiting, we would most certainly notice that.
Even if the Protheans harnessed interstellar methods of communication that did not make use of electromagnetic radiation (i.e. the beacons), it seems unlikely that there wasn't at least a brief period in which they made use of radio transmission. Furthermore, The game contains hundreds of Prothean ruins, including places whose destruction had to have been very dramatic and radiant. Such events occurred all throughout the galaxy in a span of about 100 years (if I recall correctly what Liara and Javik had said in ME3).
The only references I've found that might be relevant are the Turian space telescope comprised of Gromar and a planet in Attican Beta, as well as references to an attempt at figuring out what happened on Rothla by travelling to the event's light cone.
Is this an oversight by the writers, a blunder by the characters, or is there an in-universe explanation for the inadequacy/limitations of their telescopes?