Unfortunately, macOS Sonoma restricts access to the wifi information without Location Permissions, but does not prompt users for such permission when the wifi information is requested. Further, there is no way to manually add Location Permission.
So currently, the wifi facilities (including the Wireless Network trigger, Wireless Network condition and WirelessNetwork token) will not work with any version of Keyboard Maestro in Sonoma. To resolve this, Apple will need to either provide a way to manually add Location Permissions for Keyboard Maestro or prompt for Location Permissions for Keyboard Maestro and I am not hopeful that either of those things will happen any time soon.
Version 11 of Keyboard Maestro is coincidently planned to offer an Get Location action, which itself will trigger the permission, so when that is released (currently due later this year) that will be a way forward (and probably running it long enough to get the permissions requested and then reverting will be an option for anyone who does not wish to upgrade).
In the mean time, if you are heavily dependent on the wireless facilities, you may want to consider holding off on updating to Sonoma. Alternatively, and weirdly, as Alex pointed out in a recent query about this issue, you can use the airport command line tool:
/System/Library/PrivateFrameworks/Apple80211.framework/Resources/airport -I | awk -F' SSID: ' '/ SSID: / {print $2}'
This should allow working around the tokens and conditions, but does not help with the Wireless Network trigger.