So IIRC, you need the Apple TV to actually participate in the Fitness+ workouts, this is used to display them and as far as I know this hasn’t changed, but if it has, someone else can chime in and correct me.

The Apple Watch itself has WiFi and optionally LTE. It does like to boost off an iPhone’s Bluetooth and let the iPhone do the heavy lifting, but it isn’t required to connect to the Internet and honestly works better when it does (at the cost of battery life). So yeah, more or less, but you still need the Watch paired to an iPhone (because it is an iPhone accessory at its core), and the data is going to be logged to the Health app, and the relevant data (heart rate, workout time, whatever else gets logged for the workout) can be made available to an ecosystem of independent hardware and services. The weight my scale logs for example gets tracked by the vendor service, the Health app, and my food tracker via the Health app.

Either way, Fitness+ is a premium service, not a feature of the iPhone. That it requires specific hardware doesn’t make it particularly special in this regard either.