Which part of the Reaper activity emitted so much light that they would be able to notice it? It's hard to notice even planets when talking of such distances as 50,000 light years, never mind separate spaceships or explosions.
In the 1970's you could open up an astronomy text book and it wouldn't tell you if there were planets in other galaxies because they hadn't seen enough yet with telescopes to conclusively say they exist. In the last 10 years we've gone from conclusively finding solar systems, mostly very large gas giants to being able to see much smaller earth sized planets and enough information to say conclusively that it is probable for life to be there.
At the start of Mass Effect 1 the date is 2183, I find it highly improbable that we would not be able to see the sorts of harvesting that went on as the game describes. The Reaper ships alone disperse huge amounts of energy.
How much more effort do you think species would put into telescope technology once interstellar instantaneous travel was discovered?
The most advanced species in the galaxy at the start of the series are the Asari, and through Liara, the series informs you that any evidence at all of previous civilizations, including "light from space battles 50,000 years ago" were attributed to the Protheans. Even then, most people didn't care, and it was at most an academic and military curiosity. If anyone took notice of your lightshow at all, it probably looked like the Protheans were warring on a neighboring species.
You're making huge assumptions about the advancement in technology that aren't reflected in the fiction of the universe to prove your inconsistency, but let's review a few "facts":
- Sovereign was one of the largest class of Reapers out there. The citadel races, or at least humanity, even refer to them as "Sovereign-class."
- They saw Sovereign class energy emissions first-hand at the battle for the Citadel in ME1. Presumably every single species got their hands on that data. As far as we know, no scholars raised any alarms because those emissions and the emissions from a neighboring star system 50,000 years ago matched. They had time to study the debris after the battle, and most races concluded Sovereign was just a new type of Geth ship when they literally had a dead reaper at their doorstep.
- Even if they had believed Shepard immediately, it was only a few years between ME1 and ME3. The amount and minutiae of data they would need to sift through to get anything meaningful (now that they knew what to look for) would have been immense and ultimately irrelevant with an incoming threat.
- The idea of a 50,000 year cycle wasn't even brought up until some point in Shepard's adventure, so even if they had absolute resolution on those telescopes of yours and could see what some Prothean was having for lunch 50,000 years ago while his planet was being bombed, it would have just looked like an extinction-level event, and ultimately just something that would end up in Asari Trivial Pursuit.
- Dinosaurs went extinct 65 million years ago. That's a pretty round number. Are you saying we should we be worried?
- I think a lot of effort would be put into telescopes, in the form of autonomous satellites. I mean any scifi that has warring factions like Mass Effect whether it's Star Trek or the rest has them putting huge resources into surveillance. The Krogan rebellions went on for decades & the Geth were out hiding out during their war. I have to think that they're basically in a state of cold war, & as we know when states today are in cold war, they invest huge resources in telescopes.
- I think too much data and minutiae is a cop out, I mean they're developing sentient AI in ME for crist sake. Moore's Law, etc.