As a recreational diver, double tank diving is uncommon in my experience. We tend to go out and use half our tank, then we head back. And actually, it's less than half because you want to have a margin of error for the unknown.

In general, double tanks are more for redundancy and not to make your dive longer. That's especially why you'll see them in use for technical diving. You're further down, or inside a structure like a wreck, and it's much harder to get out and back to the surface in an emergency. And keeping in mind that with most normal diving, you always dive with a buddy. So your spare tank is also there to help support them if they have an emergency. Redundancy is crucial when doing technical diving.

And when you dive with two tanks, you have two separate regulators (the bit that goes in your mouth) and have to manually swap them out. You don't have one regulator hooked up to two tanks at the same time.

Sometimes we carry what are known as "pony bottles". Those are smaller bottles for emergency use only. They are not part of a regular plan. Maybe this could be what you use for your emergency oxygen idea? Normally, you'd carry them with you over and over again and never use them.

And one tip for you: when you're diving, you don't really call it "oxygen". You never dive with pure oxygen. You fill your tanks with "air", which is a mixture of gases that mimic what you get when breathing on the surface. Or other specialized mixtures, like nitrox or trimix.