Why does’t My ipad pro stay connected to my new iphone 13?

Stay connected how and for what? If you mean paired via Bluetooth, be aware that an iPhone will not pair via Bluetooth to a computer (Mac or Windows) or an iPad except for personal hotspot and then only if your cellular plan supports it. See the following for more information: Bluetooth: Why can't I pair my iPhone or … - Apple Community

If you are attempting to use Handoff/Continuity or AirDrop, that does involve Bluetooth but the devices are NOT paired; Bluetooth just needs to be on and the devices in range of each other. The following may help with Handoff/Continuity issues: Use Continuity to connect your Mac, iPhone, iPad, iPod touch, and Apple Watch - Apple Support