A job being your identity is a health challenge to be worked through with a therapist. Enjoy your job, for sure, but you make it your identity is to create expectations that cannot be met when unavoidable life transitions occur. A job is what you do, not who you are.
If done in a healthy way, where it contributes to but is not the entirety of your identity, yes. It's a complex topic with a lot of nuance I can't boil down into a single comment.
https://hbr.org/2019/12/what-happens-when-your-career-become...
https://economictimes.indiatimes.com/wealth/earn/why-your-id...
https://www.wbur.org/hereandnow/2021/10/05/career-job-work-i...
https://www.nytimes.com/2021/02/06/style/work-life-balance-t...
https://www.theatlantic.com/family/archive/2021/09/self-obje...