There is an excellent TED talk on the relationship between self-worth and procrastination that also, like you, makes a point about separating "me and my work" [1].
Watching this about a year ago was eye opening to me and I wished I'd found this video when I started studying in college!
Well, I have a problem here, because other than work there's not much going on in my life. No wife or kids, no fancy hobbies... I guess I really need to get more social :)
This was a big issue for me in my early 20s. I did a lot of work to ensure that my life outside of work was as interesting to me as my work life. If you don't have that balance, it is really hard to disconnect your work from your self-worth.
Watching this about a year ago was eye opening to me and I wished I'd found this video when I started studying in college!
[1] https://www.youtube.com/watch?v=52lZmIafep4