If we maintain the behaviour of depression for too long, it can lead to real depression.
So it's okay to push them and to act in their best interests as a parent. And sometimes that requires using the levers you have at your disposal.
I'd start with food and Wi-Fi.
Firstly, a rule of no food in the bedroom. To eat, you have to be out of your room and, ideally, at the very least dinner occurs at the dinner table - where you will be expected to be present for the conversation. Joining in would be great, but optional.
There's a reason for this. Research has shown a range of benefits for families that eat dinner together, from having better physical health, improved emotional health, improvements in communication skills and closer relationships within the family.
Of course, no devices, television or other distractions at the dinner table - and that applies to the adults as well.
And secondly, earn Wi-Fi access. Either turn it off and back on to grant access, or change the password daily so they have to get it from you.
If they want to get online, make it contingent on something that will help or push them - especially in the weekends. Don't punish them by just removing it completely, this can too easily turn into a stand-off.
However, make it clear they have to earn the access by doing some form of activity. That might be exercise or a family outing, or simply doing some chores. Either way, ensure you're working in their best interest, against the inactivity.
And make sure you do all of this with a lightness and a smile. Treat it like a bit of fun and be clear and open about what you're doing, and why.
Of course, also accept this means you, as a parent doing more. More relating, more work, and spending more time with them.
And maybe spend less time online yourself?
Because one of the things that has happened over the lockdowns we've likely all been guilty of taking the easy route. If the kids are quiet in their room with their device, then we get some time to ourselves too.
Treat it as an opportunity to get yourself moving as well, along with engaging with them and their world.
Because in the end, the point of all of this is to improve the connection - not to the internet, but to each other.