The wall the rail will be mounted on consists of 13mm gypsum and 12mm construction plywood. The rail could be screwed about every 5 cm, but I don't think that's necessary.
It might work but there's a risk that the hex head is too high and hits somewhere on the back of the cabinet frame.
I also advocate for round head. I bought such in bulk at K-rauta when I installed my IKEA kitchen.
I drive with convex 5x50 (6.0 works) and it holds, if you also find a rule set a 5x80..
The problem with the one you linked to is that the cap itself risks hitting the rail if you happen to set the screw too high, so you can't fine-tune it with the included washers..
I am thinking that the kitchen should hang on construction plywood. There are electrical wires running behind the wall (a lot). I will look at the pictures and see if I can hit any studs.
I can fasten the rail with 5x30 and then use some 6x25 once it's in place.
Keep in mind that you have at least 5mm material in the rail and washer. 25mm is too short. You don’t want it shorter than 35mm, as the screw is not full thickness near the tip.