Make sure you have no public or developer beta profile/system installed on your iPad.
If you do, you will need to remove/uninstall these and do a full reset/re-install and data restore, from a previous backup, first, before you csn proceed any farther.
Make sure your iPad is NOT using a VPN and if it is, disable it.
Make sure the Firewall security on your home wireless network MODEM/router is not set to fully block everything coming into it.
Instructions to modify router settings, inside the software within the router, should have come with the MODEM/router.
If your iPad is currently running a very early version of iPadOS 15, then Your iPad can certainly be upgraded to the latest iPadOS 15.6..1.
Make sure your iPad is, at least, charged to 50% or greater to attempt this.
Also, make sure your iPad has, at least, between 6-8 GBs of free internal data storage space for downloading and installing a major iOS/iPadOS upgrade.
Make sure your MacBook has plenty of space to download the iPadOS upgrade/update, also.
If you are still having issues upgrading/uodating that iPad Pro, search online to locate and call contact your nearest, “local” Apple Store location to try/attempt to make an appointment to get your Apple iPad upgraded/updated to its latest iPadOS 15.6.1 version, by Apple and Apple Store employees/Genius Bar Employees.
Apple Store employees will be glad to help/assist you.
Best of Luck to You!