According to the web page setup instructions, you will find the Apple Watch under
System Settings -> Login Password
watchOS 3 or later
macOS Sierra or later (which Sonoma 14.6.1 satisfies)
- MacBook introduced in 2015 or later
- MacBook Pro introduced in late 2013 or later
- MacBook Air introduced in 2013 or later
- Mac mini introduced in 2014 or later
- iMac introduced in 2013 or later
- iMac Pro
- Mac Pro introduced in 2013 or later
- --->>> Mac Studio introduced in 2022 or later <<<---
So the Mac Studio is supported.
So I would suggest going through each of the items in this web page to make sure they are done.
Unlock your Mac with your Apple Watch - Apple Support
Are the following true?
I am fairly sure the Mac has to be able to see the Apple Watch via the above 3 settings, or it does not offer the feature.
I remember 5 or 6 years ago when I had a company 2017 13" MacBook Pro at work, that did not show the Apple Watch unlock option. When I took the company Mac home for Covid-19 quarantine, the option finally appeared.
I'm sure the difference was the network that was at issue. At work there were lots of subnets, and the Apple Watch would talk to the WiFi network, but the iMac was on an Ethernet connection on a different subnet. I think they did not see each other. When I took the Company Mac home they were both on the same home network and subnet. At this point the unlock with Apple Watch option was available, and I have used it multiple times every day for the past 4 and a half years.