This is dependent on the type of concrete you use. With a mix that is heavy limestone (the new white stuff everyone uses for driveways) you will for sure need rebar.
If you are using a mix with a lot more aggregate it may not matter or matter enough to worry about it. I have demo'ed 60 year old steps with no rebar so many times and almost all were in great shape. The type of cement they used in the 50-60s was the best in my area and the aggregate/portland blend... that stuff lasts forever with no cracking.
I have also demo'ed 20 year old steps with rebar that the noses where cracking. I am not anti-rebar at all. I am just telling you for steps with support like yours its so far down the list of importance.
Most important things:
Set a good base and stamp it out. I have also see my old-timers add large rocks on each row that top's sit 6-8 below step.
Protect the brick that won't be part of the step. You will need some physical barriers there.
Do not use a limestone mix. Pay extra for more portland. The good stuff for steps is either dark dark grey after mixed or tan/brown aggregate mixed in. I don't care what anyone says - been through this so many times I can eye test how long concrete will last.
Floating the area is crucial and honestly it might be a step above DIY. The top needs to slightly slanting away. Each step needs to have a slight slight slant to the bottom. Each step cannot have a dip near the riser. All of this is more important going to basement steps which tend to take longer to dry out.
If you feel better add some 3/8 mesh rebar to each step. It is kind of like a craft project before your pour. The rebar should float in the middle of your pour. I am guessing you won't be using forms for the sides. So to get the rebar to float and not just settle on the bottom (useless) I have "stuck" the rebar into the high side of the dirt a good 5-8" at the right level and on the other side curl the rebar.