Long battery life >4 days: - I don’t know of any true smart watch that can do that except for Pebble.
Always on display: - Plenty, but that kills battery life even faster.
good apps inc Golf: - Any Android watch.
notifications & calendar: - Any smart watch
Android support: - Plenty
When my Pebble Steel was canceled and my replacement watch from Pebble never arrived because of the company’s sale, I ended up with an Asus Zenwatch 2. It meets all your requirements except for the 4 day battery life. However, the battery does last over 24 hours and only takes about 20 minutes to charge, so if I plug it in to charge when I wake up, it is recharged by the time I’me dressed and ready to leave the bedroom.
Personally, I wish I could get something more like the Pebble, and keep hoping that Fitbit will release something decent, but at only around $100, the Zenwatch 2 has been OK.