How do I prepare for interviews if I have a heavy workload and lot of responsibilities at work?

Sorry to hear about your mental + physical health not being well :(

In my opinion, those should be prioritized and somewhat non-negotiable. For me I work out at least 3x a week and usually right after my workday ends at 5. It helps in 2 ways:

1. Working out is super important for both mental and physical health. See here for Alex and Rahul talking about that
2. It marks the end of my workday and prevents me from staying at my desk longer than I should. If you need help with motivation to exercise, I recommend joining a class or working out with a buddy. Sports also count :) Looking into getting into a pickleball league myself right now.

Here are 2 good questions that address much of what you're talking about (one of which I asked):

1. How to balance interview prep with a job?
2. How can I have less burnout and better work-life balance?

If maintaining your work is important, then I would say focus on your work, wrap that up, to meet any impeding deadlines.

Take a few days off (2 days, that way you get 4 days padding on a weekend) after you have met your deadline, and jump start your interview prep. The initial days of interview prep are the hardest because you are training your brain to focus, solve things outside of your regular job.

Multi-tasking in my opinion is the way that one does multiple things poorly. Love the book, the ONE thing.

Another thing to note, what jobs can you outsource? Food delivery? Office tasks? Instacart? This can free you up from some mental load.

I'm sorry you are going through a rough phase, do something that brings you joy for 30 mins -> non- negotiable!

Are you able to talk it out with someone? Meet people you are comfortable sharing?

I hope you feel better and your circumstances improve.