Does PNG files size affect video output file size? I’m creating 15 second animations with approx 500 frames (1280x720) at 24FPS resulting in 20Mb file size. Similar videos online are well under 5Mb even under 2Mb. I’m currently video editing using the default blender settings for 720p MPG4 H264 with no audio. I tried various video output settings to reduce file size but there is a noticeable drop in quality. 

My initial PNG renders are at blender’s default settings but with 100% compressed RGB (no alpha) with each image about 1.2Mb. Would compressing these images further in blender or using other programs etc reduce the video output of these images? Or is there no correlation between the PNGs and MPG4 file size?

Either way, what are the ideal PNG and video output settings within blender to reduce the final video file size whilst maintaining the same quality? Or should I be compressing the videos further using an external program?
Yes...and no.

First of all, I would 100% recommend that you render at the same resolution that you plan to make your video unless you're planning on using AI Upscaling. Doing otherwise would result in the same effect that zooming really closely into an image produces - you start seeing the individual pixels.

Video files will always be smaller than the summation of the frame outputs. That's because videos don't actually store every single frame as an image, they instead use algorithms to store some frames and record what changes between different frames. Rather than trying to explain this myself here's a good short video explanation for this by Tom Scott on Youtube.

From my experience (and it should be noted that I've done some video editing using Adobe Premiere in the past, but nothing professionally), you shouldn't need to further compress the video - MPG4 will already compress the output to be much much smaller.