I found a fix for my full screen problem without mods.
Option 1 - If you have a 4k display, lower your resolution to 1080p. In the game graphics menu set the game to 1080p and window screen to Full-screen. This is annoying because you gotta do this manually every time you want to play the game.
Option 2 - Open AMD Software Adrenalin, go to Gaming Setting, Look for your GOG Metal Gear Rising, Radeon Super Resolution must be enabled to borderless Full-screen 1920x1080, I put Sharpen Effect to 80. On Display make sure you put Scaling Mode to Preserve Aspect Ratio. On the Gear setting look for display make sure GPU Scaling is enabled, scaling Mode to Preserve Aspect Ratio. In the game graphic Settings you can now set the game in Full-screen 1080p! See attachments for this option.