The M is to put the transmission in Manual shift mode and the arrows are for shifting when in the manual mode.
Tow haul is for use when in Automatic shift mode. This mode keeps the transmission in lower gears longer when accelerating at lower speeds or in rolling hills. It impacts shifting and serves no purpose when up to highway speed on the interstate.
The general rule is to use tow haul when the trailer is at 75% or more of the vehicle towing capacity.
I’m surprised you didn’t find a clear explanation in the Chevy owners manual. My experience is with GMC and our owners manual has very clear explanations for the operation of tow haul mode.
