I looked at your game screenshots again. I'm not sure how you have 4k textures being utilized other than UI.
Here are some more general pointers, just in case.
- Group your textures into a texture atlas logically (such as a UI atlas, an Enemies atlas, a Player atlas etc).
- Proper grouping will allow you to batch your draw calls without having to change the texture state.
- Make sure that if you are drawing something at a size of 64x64, you are not utilizing a 256x256 texture on it. That is overkill and it will affect performance. Generally for 2D games, you want the texture size to be close to the object's size. If they are a perfect match, you will see "pixel perfect" results.
- If you aren't already, for UI, try to implement reusable textures and Scale 9 grid (like in Flash).
- Instead of using unique textures for all solid colors, reuse a White 1x1 texture and blend your solid colors on to it using vertex color blending.
Good luck with your project!