The partner who didn't give birth is there to take care of two mostly helpless human beings, one who just came into to the world and one who needs rest and TLC so they can rejoin the world quickly.
We're talking about human beings. Efficiency is not part of the equation. The perinatal period is the most physically (and very often mentally as well) dangerous period in a woman's life. Women to this day die from complications in childbirth.
The first six months after birth are incredibly difficult on a woman's body and mind. Women NEED their partners' help at this time, efficiency be damned.
Maybe it’s just the phrasing of this and it’s intended differently, but it seems like terrible advice. You should never put your own mental health last. If you’re in a hole you’re not going to be able to help anyone else. If OP has just found out they’re having a baby they likely have some time. If they use that time to focus on themselves and get themselves in a better position they can be in a much better mental state to help when the baby actually arrives. The statement I quoted reads like the OP doesn’t matter and he should accept that. But maybe I’m not understanding your intention fully.
His post expresses a great deal of anxiety over his financial circumstances and job performance -- which are valid, and, importantly, are problems that can be solved later. My intention was to convey that fretting about finding a new job or improving current job performance are NOT where OP's energy should be going right now, even if it seems on the surface like a new job will solve all of his problems.
OP should focus that mental energy on:
a) getting parental leave so that he can b) improve his mental health and c) support his partner and his new baby.
Good luck, OP! Just remember that you are not the only person who has ever become a new Dad, and you are going to get through this! I'm wishing you all the best for your family!
Do whatever you can to get as much parental leave as you possibly can. Be there for baby and mama, and then -- only then, after baby is a few months old and your partner has healed a bit -- should you start worrying about your job and finances.
Thinking about caring for your new infant and partner's perinatal health are enough work already, and are far more important right now than your job anxieties.
The only solution for you right now is to understand your priorities. At the moment, the only thing that really and truly matters is your wife/partner's health and your baby. Focus on those for the first month.
After that, focus on the job.