... adding how their daughter seized and her heart stopped ...

[user_user]

19-year-old Wis. college student with peanut allergy dies after eating gluten-free brownie: ‘She was completely unresponsive’

“The second bite, she knew something was wrong,” her father said.

nypost.com

“She was completely unresponsive and I was incredibly helpless,” her family said, adding how their daughter seized and her heart stopped for several minutes in the ambulance before arriving at the hospital.

Question: Does "how" here mean the same as "that"? Like, "said that~", "added that~"? It definitely doesn't mean "the way"?
I really often hear native speakers say "how" instead of "that" like this.

 

[Tarheel]

You already know the answer to the question.

You could indeed use "that" instead of "how" there.