Logged into new Apple ID on existing device, won’t change saved things.

I have had the same iPad for a while, and when I first got it it was connected to my mom’s Apple ID. I put off changing them because I was worried about losing all of my art on Procreate. I discovered recently I can transfer it all over if I save the files locally on the device. I did that and logged out of the old one and into mine.

Here’s where I’m running into a problem: I’d like my phone’s contacts, messages, and calendar to sync to it on my phone, but it’s still synced to the old Apple ID (it’s connected to my sister’s phone) How do I get all of that data synced without factory resetting and losing my local procreate files?