What is the mental or emotional status of being in “mom mode”?

She was posting a pic of her kid instead of ranting about her loss.

It does not sound sexist to me and is understandable English.

https://twitter.com/serenawilliams/status/1037879968104165376

It refers to her activity, after the loss, on Instagram about her daughter, suggesting she was in mom mode (caring about her little one)

Williams’ only message Saturday night was a brief Instagram video of her 1-year-old daughter Olympia, wearing a miniature version of her mom’s tutu and little sneakers, toddling with her beloved doll, Qai Qai.

Washington Post

Mommy mode is a more used expression on the net. The expression refers to the multitasking ability that moms appear to have in taking care of different things at the same time.

I now know the true meaning of “mommy mode.” As mothers, we tend to use the term loosely. What does it mean to me? Mommy mode is when you have to multitask to get 10 things done at once; when you don’t care how you look doing it, as long as it gets done; when energy from deep down in your body kicks in to help you get it all done.

The expression, according to Google Books appears to be from the late ‘80s/early ‘90s.

From Until Death Do Us Part Christine McGuire , 1996:

Kathryn quickly scooped up her files, her mind already going into Mom Mode, as Dave called it. Between now and the time she picked Emma up from school and dropped her at her violin class, she would consciously shed the formal identity of ...