Question about size of textures

I’m trying to understand how to best create a texture for my model.

I made a vehicle, and creating a texture for the body (so no wheels, engine and suspension) requires me to basically create a 8192 x 8192 texture to get the level of detail I want while texture painting. (That is because when unwrapping there are so many UV islands that each one is pretty small when I use a 2048x2048 or even 4096x4096 image). That in turn makes painting small details impossible because it’s too low resolution.

That made me think that maybe I need to have separate images for the body and things like doors, the hood and so on so that I don’t need that big of a single texture.

That however seems like a pain when doing texture paint or baking textures/ambient occlusion/dirty vertex colors because it sounds to me like I would have to do that individually for all the parts. Or can I select all the parts and do it with all of them at the same time somehow?

Can someone explain how I would best go about doing this?

Is it alright to use a really big texture while painting, and then make it smaller later? I have no idea how to approach this the best.

Tl;dr: Unwrapping car body onto 2048x2048 image causes brush to be pixelated when painting on details. How do I go about creating a texture for this that allows me to paint small details?

MAN id like to see the pics 8192 is quite large!