It should work fine, PCIe over Thunderbolt foo is relatively simple. Many many people here use these Apple Thunderbolt 3 to 2 adapters with the Thunderbolt Native box.
The display warning you are worrying about is not relevant here. Thunderbolt 1 and 2 used a Displayport connector instead of the USB-C connector used in Thunderbolt 3 and 4. All the warning is pointing out is even though the connector look the same you can't plug this Thunderbolt adapter into an actual Displayport port and expect it to work. And what is going on with display over Thunderbolt is different to PCIe data over Thunderbolt.
But note that one user on DUC reporting having problems with Native on a Mac Studio with a Lynx interface (which may or may not be relevant) on the Mac Studio, not clear of the cause:
https://duc.avid.com/showthread.php?t=419428 another user in that same thread reporting Native runs fine. And we are maybe getting off track there with HD native PCIe vs. HD Native thunderbolt.