How does one go about switching to a new bank account?

I recently opened a savings/checking account with a credit union so that I can get a credit card there with a lower interest rate, and down the road a lower-interest rate auto loan. Who knows, maybe even a mortgage one day.

I have had the same checking/savings account with a big bank since I was like 19 (I am 30 now), which everything I have on autopay/payment apps/amazon, essentially everything is linked to. I also have 2 credit cards with a different large bank.

I don’t have a ton of money in savings and I’m worried about switching my paychecks to my new account out of fear that I’ll somehow overdraft my old account on some autopay/card linked purchase situation 🤦🏻‍♀️

Ugh I wish there was a step by step manual for things like this.

Can an adultier adult please help me come with a plan so I can get this done? Or anyone who is good at financial stuff? I love my parents but they didn’t teach me hardly anything about finances and have been with the same credit union for 30+ years.