Our cats ( BSH and a Chartreux ) have always been 100% indoors, and nothing changed when we moved them over with our German Shepherd to Brisbane. Domestic cats tend to kill native birdlife, so being indoors is the right thing to do over here.
Cats are usually pretty easy going when indoors, as long as you keep their kitty litter tray regularly cleaned and food and water refreshed. Our cats are part of the family and love hanging out with the hoomans. During the day they don't do much anyway, apart from sleep in their fave spot by a window and will be happy to see you when you get home from work for a snuggle. Mine always jumps up onto my lap for cuddle time while I settle down for the evening to watch TV in my fave chair.
In short, cats are totally happy with living indoors.