Do not vape. Vapes are made from plastic, some small electronics, and a lithium-ion battery. The plastics and metals are currently too difficult to separate for recycling. The plastic is likely to be too low-grade to be used again.
Most importantly, lithium-ion batteries are very difficult or even impossible to remove. Recycling them is often too expensive to do at scale because it takes so much time and effort to remove the battery. They have to be done at hand. Think of 1,000 vapes in a recycling centre.
Lithium batteries are volatile and explode if they are put through recycling machines. So, vapes are likely to be thrown into landfill.
If you do want to vape, please remove the battery when you're done and recycle it at your local battery recycling centre.
If you can safely pull apart the metals, electronics and plastics, the metals and electronics can be recycled. It's better than all of it going to landfill...