Your looking at the difference between mountain bike pressures and speed and road pressures and speed.
You will be fine patching a tubeless tyre. Maybe stitch it with some dental floss, nylon thread or fishing line if it is bad but otherwise just patch with a big standard inner tube patch on the inside. I’ve been running a tyre with a 8mm cut clean through like this for around 6 months as the tyre was new when damaged.
However, running 100psi and regularly going over 40mph means I’d buy anew tyre for the road bike unless it was purely superficial in the very outer layer of the main carcass of the tyre.