Before Jesus died on the cross, his body was functioning as of that any other human being where he was breathing to stay alive and then he took his last breath and died. Then rose from the dead and his body could appear anywhere at any given time. Since Jesus rose with the same body that was crucified, was it subject to natural laws of requiring oxygen to survive because some disciples gave him fish to eat and the holes the Romans punched in his feet and hands are still visible. Given that Jesus is sitted at the right hand of God, does that body require oxygen to stay alive or the power of God sustains that body?
It's agreed by pretty much all Christians that our bodies after the resurrection will be different from the kind of body that we have now. The primary source for this is 1 Corinthians 15
Not all flesh is the same: People have one kind of flesh, animals have another, birds another and fish another. There are also heavenly bodies and there are earthly bodies; but the splendor of the heavenly bodies is one kind, and the splendor of the earthly bodies is another. The sun has one kind of splendor, the moon another and the stars another; and star differs from star in splendor. So will it be with the resurrection of the dead. The body that is sown is perishable, it is raised imperishable; it is sown in dishonor, it is raised in glory; it is sown in weakness, it is raised in power; it is sown a natural body, it is raised a spiritual body.
Nothing is specifically said about whether those bodies need to breathe or not. It depends if nothing else on the nature of heaven, about which we are also given few details.
God was already breathing before he created us out of the mud of the earth. He breathed into us the breath of life which implies that God lives and draws the breath of life.
And the LORD God formed man of the dust of the ground and breathed into his nostrils the breath of life, and man became a living soul.
Given that the Lord God of the old testament is Christ then he draws the breath of life which is different from the breath we draw but he breathes
We see in Jn 20:22 Jesus appearing to the disciples after the resurrection and breathing on them saying : " Receive the Holy Spirit ". So, it was the Holy Spirit that the resurrected Lord breathed in and breathed out. In case there is oxygen in heaven for all the souls to breathe, there will also be trees and vegetation to replenish the breathing air. But, the teachings so far do not tell us that trees and grass grow in heaven !