Question on Studio Camera Features

I understand that using a combination of an ATEM and a BM camera allows for, among other things, live color correction. I'm curious, though, whether color correction in any form is available on the cameras themselves without the use of the ATEM, and/or whether the camera can be hooked up to an ATEM, color corrected, and have that color correction remain persistent after disconnect. Is this a thing?
The set-up I'm working with will soon include wireless cameras, which means no return feed. It won't do to have some cameras color-corrected and others not, and we're looking at upgrading to studio cameras from generic Sony DSLRs.

Thanks for reading!

LUTs are the answer to all your questions

The color corrector on the camera is internal, though only WB and tint are available at the camera. The corrector can be accessed from an Atem or through the Rest API. Color correction settings can be stored in a camera preset.

LUTs can be helpful when the cameras support them. If all the cams are similar then a preset LUT can be helpful, though likely unnecessary if they're all the same. To create a LUT from scratch you need to create a baseline image then match all the cameras to that reference. To match different cameras with any real precision takes a little skill and understanding of colorspaces, grading, and camera color matrices.

Good Luck