Epoxy or superglue? What's works best to attach a metal bolt sleeve to a chair?

I’d use 5-minute epoxy. It will fill gaps better than superglue, if the fit is less than perfect, and be less brittle once it sets. I recommend the 5-minute stuff, because the slower setting epoxies can have time to soak into the wood grain before setting.

I second epoxy. Superglue doesn’t really work on either metal or wood; one is too porous, the other not porous enough.

Epoxy

An epoxy solution is probably your best solution, but gorilla glue is another alternative. It fills gaps in the wood aggressively and holds pretty good. Strengthwise it is a step down from like JB Weld, (the handyman’s other secret weapon) but I do like that it bonds very well to metals and woods.
Another solution is inserting another sleeve. You overdrill the hole to 5/8” and screw the sleeve (liberally coated with JB Weld or Gorilla glue) into the wood; and you will have a mechanical connection as well as an adhesive connection. I recently did something similar in a fiberglass roof on my little Miata and it is holding really well.

Epoxy: specifically JB Weld.

THank you all. JBWeld and a new sleeve tomorrow.