Unless the painting paper has plastic or tape, in Other words, is not all paper with no coating etc, to stop it from rotting, I would use either. Newspaper, (non-glossy) is great too, and free, if you go where they dump it off to recyle, or you get a paper anyway. The newspaper is a bit more work if you get some breezes, or lots of wind that day when you try to use it. I have used it to expand beds, just put down a heap of mulch to hold corners down while using and when done cover all the paper with mulch or soil, whatever you want to use for your plan. That's my 2 cents anyway. I use about 6 pages thickness for each joining piece coverage.

Kraft paper, that brown paper sold now as painters paper once was known as butcher paper and is the same thing as what is sold on line as mulch paper. This is the same paper used to make the bags of all sizes that we carry
"stuff" in. I am also seeing some places substituting "painters paper" for art paper, the paper artists paint on or use for mattes and some of that may be kraft and some not.
You may find some stores sell a coated (non plastic) paper as well as an uncoated paper and you would want to opt for the uncoated.

thanks everyone, those were my thoughts too. I love newspaper but the way our recycle center is now set up I don't have access to it so I'd literally have to hang around the bin until someone came by.

This may not help you, but.......... There are dumpsters in some places that are for paper only. Newspaper mostly, and you can likely get stacks of Newspaper or other non-coated paper.

Removing material left at the recycle centers by someone other than an employee of the owner has resulted in misdemeanor theft charges being filed against that person removing, without permission, the material. That "trash" that is put there is a source of money for the owner of the recycle center.

We have dumpsters away from recycle centers, along a road here and there, one company "paper retriever" has them in a couple places. Nobody should risk a fine, but these are off the road, with no cameras. I will risk it myself. My mom dumps off glossies, and I retrieve newspaper. Just my POV.