Hey there,
not sure how your system is setup but as ffor your question. 2000x2000 px textures are not that big and there shouldn’t be big performance problems if things are fairly setup.
So for textures I recommend power of 2 (2048px) it is a good practice to use power of 2 images.
How many textures are loaded during a level let’s say ? is there a system already for them to be loaded on the background? Like when animations etc about to finish for one image, in the background other image is async loaded.
Here is a data loading method
You can make a table of images for a level let’s say and you can async load images during play on thee background so they are not kept at memory.