I don’t think slate will stand up well to being driven on.
It will crush up into small, surprisingly sharp shards quite quickly.
As stated hardcore lightly tamped, barrier,then gravel of your choice.
A rough edged gravel will eventually pack down hard. A pebble type will stay loose and may need raking back every now and again, as it shifts a bit.
Gravel also avoids the planning for water run off(i think thats what they called it). But this is relative to how much garden you have to soak up rain, compared to roof/hard standing area. I believe.
I graveled my back garden instead of slabs after council advice/restrictions.