Do I turn off my old IPhone prior to setting up my new IPhone

Perform the transfer using the transfer sequence documented by Apple, and the tool will tell you what to do for your case.

Transfer data from your previous iOS or iPadOS device to your new iPhone, iPad, or iPod touch - Apple Support

Whether the SIM gets extracted and transferred, or the carrier electronically relocates the plan in the carrier database, or the carrier now uses an eSIM will vary by carrier, and by the particular carrier situation.

There’s a debate around whether powering down is necessary or not. Hot-swapping the SIM won’t cause damage. But it might require a restart to start working.