An engagement session can be between 30 minutes up to about 2 hours or more. Most engagement sessions I photograph are 1 hour. 1 hour seems to be a good amount of time to get a variety of photos at 1 or even 2 locations sometimes. That would also include a possible outfit change.
I pack my bag differently for each photo session I am doing. For weddings, I am usually bringing a lot more gear than with an engagement session. It is my goal to keep things minimal. Being minimal helps a lot so that you are not lugging around tons of gear. It gives you the freedom to not feel constricted with bags and straps. Just you, your camera and your couple is so refreshing.
With that said, I will bring the following
Sony A7iii with a 24-70 2.8 lens loaded with a 32 gig memory card and a full battery. I have my trusty camera strap attached. I also have a flash trigger on top just in case I need some flash to fill in light during the shoot.
In addittion to my main camera, I always bring a back up camera loaded with a card, battery, and strap. Ill bring a few extra batteries and cards with me as well.