I think you will find a skirt on surface under the gravel a good investment.
And it will be much harder to install once you have the gravel!
Honestly if cost is an issue I would skip the gravel until you can afford to add it on top of a hardware cloth skirt.
One suggestion. Do a daily walk around the perimeter so you. Am see if anything has been digging.
Also, you can do a skirt in the surface relatively easily (I mean without digging down) and just lay the gravel on top.
I have a dirt floor.
In the run I get some wet patches and in those areas everything composts down nicely and the chickens find lots of worms and beetles.
Inside the ‘house’ part it is dry. Too dry really. Sometimes I hose it down!
The dark soil you showed won’t be an issue. It isn’t like...