Or are “work” and “play” terms for the left (analytical, procedural) and right (creative, random) sides of the brain so we’re balancing both all the time?
What books about this have you read and recommend?
Which companies have the best balance of work and play?
Consider:
Creativity - https://www.youtube.com/watch?v=Pb5oIIPO62g
Flow - https://en.wikipedia.org/wiki/Flow_(psychology)
The idea of working and playing at the same time is a bit fantastical. It's true you can flow, you can be creative, while working, but that's not play, and for probably >95% of workers, work won't be play. Work may be meaningful and purposeful, but really it pays the bills and provides meaning/purpose.
Play is something we associate with children and puppies/kittens, with games and sports and make-believe. Play is an enjoyable amusement which might mimics real-life tasks and skills in a safe environment. Work is real, and it isn't going to be low-pressure and fun for almost all jobs, otherwise why would they have to pay us to do it?
I'd look at finding true depth in the work you do, so you're finishing projects on-time, with high quality, in a non-distracted way that enhances your meaning/life. Then you use the ample spare time left to play.