I don't understand how one can be bored in this situation.
You can learn a new language or to draw. Read novels. You can start writing a program or a blog: write it on a different computer, but you are in this situation nobody cares anyway.
You can listen to podcast, even binge watch a tv show discreatly.
You can practice maths, go back learning things you wish you spent more time learning in school.
You probably can even start a business if you are careful no to leave trail.
But also: you can put money on the side, and prepare to leave.
It takes time to transition and get in the headspace of doing something new.
Every time I’ve had weeks of open time to myself the first few days/week is getting oriented. It’s only after being bored for a while that the really exciting stuff comes.
Also when you’re expecting your situation to change “any day now” it dampens the energy to start something new and ambitious.
Yes, this and also you're wondering/worried about where your income is going to come from. Having to job-hunt when you are about to be unemployed is a lot more stressful than doing it while you still have income. Unless you've been able to save a sizable emergency fund, that is going to be weighing on your mind.
The pretending part is the problem. As soon as you have requirements like answering on a chat, replying to email within a half-day of work, sitting at your desk, using corporate hardware... it adds mental workload and physical constraints that drastically reduce your options.
You underestimate the likelihood that you are being watched by colleagues in the same position who are more than happy to maintain the status quo.
See my comment above.
You can learn a new language or to draw. Read novels. You can start writing a program or a blog: write it on a different computer, but you are in this situation nobody cares anyway.
You can listen to podcast, even binge watch a tv show discreatly.
You can practice maths, go back learning things you wish you spent more time learning in school.
You probably can even start a business if you are careful no to leave trail.
But also: you can put money on the side, and prepare to leave.