The Private Wi-Fi Address feature has existed in iOS (and its variants) for several years now, but was just introduced on the Mac in Sequoia. It's not an on/off setting; the options are "Off", "Fixed", and "Rotating". In most cases, the default is "Fixed" β your Wi-Fi interface has a fixed, unchanging MAC address for each network you join, but it's different for each network (according to Apple, "your device chooses Fixed by default when joining a new network that uses WPA2 or stronger security").
Evidently some software uses your Wi-Fi MAC address* to decide whether it's still running on the same machine (as an anti-piracy measure). I don't think this was ever a good idea, but it's definitely going to be a problem for users who join different Wi-Fi networks, since macOS uses a different MAC address for each network you join. If you have software like this, you'll have to set Private Wi-Fi Address to "Off" for each network you regularly join (at least the ones where you use that software). But you should also contact the company and tell them to stop doing this. MAC addresses are an easy way to track your physical location as you join different networks, so software should no longer rely on them for authorization.
Here's an Apple support document with details on how the Private Wi-Fi Address feature works:
https://support.apple.com/en-us/102509
* For those who don't know, a MAC address is a "media access control" ID that every network interface has; it's not a "Mac" thing.