This is all just speculation but it sounds like you're connecting your Gear S3 Frontier smartwatch to your S22 Ultra phone via Bluetooth connection, not WiFi.
With WiFi, it's going to be your home router that emits a WiFi signal that your various devices will use for wireless networking connectivity. Or in other words, your router is the gateway for your home network, all your devices connect to each other directly through the router.
With Bluetooth, it's going to be your S22 Ultra that emits a Bluetooth signal. It won't support multiple devices concurrently, you can have multiple Bluetooth pairings but each one is just one device to another device wireless connection. And Bluetooth is a weaker signal than WiFi, with less coverage range and slower bandwidth.
Still, you should be able to get a usable Bluetooth signal a lot longer than 10 feet. But there are most likely a lot of variables that need to be accounted for. Wireless signals are prone to any number of interference and obstacles -- solid brick walls or stucco, metal ducting, a lot of kitchen appliances emit a lot of electromagnetic interference that's close to the same frequencies Bluetooth is based on, or the position/location of where you leave your phone when you're in the kitchen.
Anyway, do you have your Gear connected to your WiFi network or just using Bluetooth?
If WiFi, what kind of router do you have?
As for your query, I'm only guessing but an upgrade to a Smartwatch5 Pro would most likely be an improvement, it has better WiFi support and a newer version of Bluetooth. But I still think it there's a question on how you have your Gear connected that's a determining factor.
