Back when I was young I had to install sidewalks as part of my construction job. I found that preparation was as important as the actual pouring for a sidewalk that looked good over time. One of the deciding factors in your application is your climate. Do you get a frost layer during the winter. Since I don’t know this I will give you some general guidance -
First, rent a motorized soil compactor. Go over the area many times. It will now have settled and need some more fill so use sand for setting paver bricks. This is available at any big home improvement store. Fill and compact and then compact some more. Settling substrate is what ruins most patch jobs.
I would then put in a layer or two of concrete reenforcing wire. Also available at the store.
I would then moisten the base sand just before pouring the concrete. Remember, you don’t want the cement to dry out, you want it to “cure”. The slower it cures the stronger it will be.
After it sets up you can use a broom or trowel to make the surface match the existing walk.
The rebar is pretty much optional but it would just be another layer of protection if you are able to work with it.