Unfortunately on the new 7 Ultra Wi-Fi only turns on when it is deemed necessary because it supposedly uses the Bluetooth connection to the phone. Unfortunately I often find that my Google Assistant and my Google Voice typing will not work cuz it says not connected to the internet. I fixed this by opening developer options and turning off the automatic Wi-Fi connection. Then I went into connections and turned on the Wi-Fi. Now my Wi-Fi stays connected all the time. I don't know what effect this will have on the battery yet but time will tell. Hopefully Samsung will fix this issue on their own. I did not have this problem with my six classic.
This will only work as long as your watch is connected to a wi-fi connection with an SSID with or without a password. If you are in a public place, like a restaurant or airport, or even your carrier's hot spot, the watches are not compatible with that, because you cannot open the required web page to grant permission to use it. It took me a while to figure out why, while I was in a place with a connection like that, I couldn't access my Google keyboard's voice typing on the watch to answer a text. It was at that point I realized it was because the venue I was in had one of those types of wi-fi connections. Once I turned on my data connection (I usually kept it off), I was able to access all that again. It doesn't need wi-fi, it needs a connection, and a data connection works just as well as wi-fi--I believe it uses less battery energy as well..
