You can lead the horses to water but you can't make them drink. Keep offering to hang out, maybe if you're having a deep conversation ask if this is how they want the rest of their lives to go and if they have ever looked into mental health help (this absolutely may be them struggling to do things and not letting themselves think about that fact). But at the end of the day you can't improve things for them, you can only offer whatever help you can offer, help if they ask for it, and provide a good alternative.

Also, encourage them to take regular walks. It's a really good first step to stopping being a shut in. It involves changing scenery, exercise, and places you around other people. Biking or running would be a next step if they're interested, they can serve as a hobby and cardio and biking can also be a form of transportation around town as well as providing an opportunity to get involved in social rides. Things like that drastically impact mental health