Apple Watch on watchOS 7 beta constantly logs into wifi as new device (gets new ip address)

I'm not sure how knowable about networking you are so sorry if I'm explaining basic stuff you are already aware of here.

Typically home routers use a system called DHCP (Dynamic Host Configuration Protocol) to automatically assign IP addresses to devices as they connect, these addresses are limited in number so your router "leases" them to each device for a set period of time and the router may revoke the lease at any time should it need to, this ensures it will not run out of addresses.

In some cases lets say your Mac was given an IP address, but it stays at home all the time, it may always request extensions to its lease and so it's IP address may appear to never change. While devices that come and go may change IP address more frequently. Devices can also request new leases for other reasons too and not necessarily request to keep the same IP address.

If it is simply the case that the Apple Watch is being assigned a new IP address frequently, then it's probably just that the DHCP server in your router is suppling it a different IP address every now and again when its lease is renewed. It could be that there is something in the code of watchOS that is causing it to request a DHCP renewal more than it used to. I wouldn't worry about it for now, it's beta 1 after all.