Will it work with a Garmin, WHOOP or Oura?

Only via Apple Health, and only for what those devices write there: workouts, steps and active energy. HRV, resting heart rate, stress and Body Battery do not come across, and there is no direct API integration with any of them. The only direct vendor link is an optional outbound one to Strava.

Is an Apple Watch required?

For readiness, sleep and the training-adjustment loop, effectively yes. Strength logging, nutrition and the coach work without one.

Does it actually change the workout, or just advise?

It changes it. The intensity ceiling is applied to today’s entry in the weekly plan and travels with the generation request, so the session produced is already constrained. The athlete sees the proposed change with its reason and can decline it, and an explicit request for a specific session overrides the recommendation.