Transfer from Mac Pro 2013 (Monterey) to Mac mini M4 ( Sequoia)

Thunderbolt 4 isn't backwards compatible with Thunderbolt 2: to get TB2 devices working on TB4 equipped computers you need a dock and adaptors. 

A better strategy has been suggest by @tbirdvet and also from apple

Transfer to a new Mac with Migration Assistant

" The steps in this article describe how to transfer content from one Mac to another Mac over Wi-Fi. It's also possible to transfer content from a Time Machine backup, or from a Windows PC, or from an iPhone. "

According to this, About the Apple Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter - Apple Support , the adaptor should work.

"You can also use the Thunderbolt port of this adapter to connect an external hard drive, dock, Mac, or other device that uses a Thunderbolt or Thunderbolt 2 cable for data transfer. This adapter supports data-transfer speeds up to 10Gbps with Thunderbolt devices, and up to 20Gbps with Thunderbolt 2 devices."

However connecting two Macs directly can sometimes not work as smoothly as an external drive. As others have suggested, make a Time Machine (or "clone") backup of your old Mac and connect that drive to the new Mac for the migration, that has always been the most trouble free approach in my experience.

First, I would use Time Machine backup to transfer all to the new Mac. I recently transferred my Monterey backup (from my 2018 Mac) to my New Mac (2022) but it was Sonoma at the time. The only issue I had was that 3-4 apps would require I re-enter my license key to operate once again. otherwise I had no issues. The old OS will not transfer so no worry there.

Not sure about any adapter. Never try wireless as it cannot work 100% of the time. Like I stated the easiest and most fool proof is to use a TM backup drive to migrate.