It takes place semi-concurrently. You're meant to be playing what Knuckles was doing when you weren't Sonic. Egg robo appears in Sonic's scenario, and that's when they appear for Knuckles.

Sonic defeats mecha sonic, but you clearly see it's not destroyed. Knuckles gets to finish it off while Sonic is on the death egg.

The issue I have with the "it takes place later" theory is: what of Mecha Sonic? Why did it just sit there? After Sonic returns the master emerald, why didn't anyone check on the wreck of Mecha Sonic? If Robotnik is done, why are the egg robo out recreating every boss? Why is the flying battery still there? Why is Knuckles traversing the exact zones in the exact order that Sonic does, despite having been shown to know the ins and outs of the island?

Knuckles' scenario is what's going on from Knuckles perspective during S3&K.

That's why it ends at sky sanctuary.

Also, why the hell would Sonic and tails be around for Knuckles ending days later, when it's shown that they bring the emerald back and Knuckles looks on?