Weird graphical issues with lighting after upscaling

Is anyone else experiencing issues with in-game lighting after upscaling? I notice that lights become extremely bright, have blocky textures appear around them, and look muddled when upscaling past the native resolution. Note that playing on a native resolution solves the issue, but playing games in 720p in pretty unbearable for me nowadays, so I'm hoping I can resolve this. Another thing to note is it seems to only affect games with complex lighting effects.

I think you mean while rendering at higher resolutions, upscaling shouldn't affect how the game is rendered since it's just upscaling with bilinear, nearest or FSR from rendering resolution.

Either way, without any details, cannot guess what is the problem here.

I'm sorry for not providing further details. Let me provide some screenshots to better explain my issue.

Here is a screenshot of the main menu of Singularity being rendered at the default resolution:

   

And here is the main menu being upscaled to 1440p:

   

Notice how the swirling light in the background suddenly changes in shape and appears to have blocky artifacts? This similarly happens to all lighting effects within the game when upscaled at all. I was wondering if there is a way to fix this or if it's just a product of upscaling past the default resolution.

Your screenshot is at 720p. The game is not upscaled, it's downscaled to 720p, assuming you're rendering at 1440p.
Again, you are mixing upscaling with higher resolution rendering, they are not the same thing.
Upscaling does not introduce any issues since it's post processing after the frame is already rendered.

For solving these kind of issues when rendering at higher resolutions, you can try different values for Resolution Scale Threshold. If you want to be sure the setting fixes it, try 1024x1024 off the bat, then lower it until you find the lowest value that doesn't cause that corruption.

You can also try to turn off Anti-Aliasing, and ensure AF is set to Auto. If these don't fix it, then it's likely there is no solution at the moment.
Some visual bugs with higher resolution rendering are known, but no solutions exist.

The game is built on Unreal Engine 3, try setting the Resolution Scale Threshold to 256x256 or 512x512