'way of working' is a perfectly correct and usable phrase in written English. You can use it when referring to a particular method or style of working, such as 'The team updated their way of working to be more efficient'.
Things have a way of working out".
"Every manager has his way of working".
But I like that way of working.
It's a very different way of working".
It's a different way of working.
It's a whole new way of working.
His way of working is certainly effective.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com