I presume your tire liner acted like a boot. Still, that is a pretty big gash, full thickness.

I can't say whether I'd try booting and remounting (rear) or just toss. You are already quite worn down.

One thing that I do is check the tires for glass, wires, and thorns before remounting. So, I'd probably have picked up that gash as part of my routine check and removing debris (I don't do it as regularly as I should for tires that are in use).