Hopefully zero! Still, if you replace your car (or its battery) every 10 years (pretty long IMO) and smoke one vape a day (yikes), you'll use more cells on your car than your vapes.
I would hope that too. I imagine that as long as the pack still works, most cars will be sold forward on the used market. If the pack fails (either due to cell death or a crash or whatever), I bet many of them will not be properly recycled, especially from the early days. Once most cars are EVs, recycling will probably get better.
Either way, it seems pretty unfair to assume that EV packs will be 100% recycled, while vape packs will be 0% recycled. One could imagine a sort of "core charge" for disposable vapes. Bring the vape back for recycling when you get a new one and get $2 off. This could even be done by law like California CRV for cans and bottles.