The soul is not the body. Lazarus was the body; that was dead. In the other passage, 'His breath goes forth, he returns to his earth....' -- I would interpret this that his soul went forth and the body returned to the earth.
Not everyone lives from the Bible -- there are many religions and many books, most of which have been altered through the centuries to suit those in power. I believe that, originally, there was a set of guidelines for living here but those guidelines have become quite 'fuzzy' over the centuries for various reasons. The Bible and other religious books are used to control people, so that they will not think nor experiment for themselves. If everyone believed in reincarnation and numerous lives, then the religious bodies might have a difficult time getting people to 'tow the line'. I like to follow the philosophy of treating others as I would like to be treated.
Thousands and thousands of people have out-of-body experiences where they travel far -- to elsewhere on earth or through the Universe itself; some go to other dimensions.
Although the physical body may still have some functioning going on, the soul has left and gone on its way. The animating energy is gone. The rest is just the using up of the physical nerve and cell energy.
MH on Ask the Barefoot Herbalist forum says that throughout the last month of his father's life, his Dad was more less 'out of it'; however, at some moments when he was talking, he swore a lot. MH says that his Dad never swore, not even if he hurt himself, so he figured that another entity had taken up his body at times. Then, when his Dad was himself (no swearing), he told his son of all of the places that he had travelled -- so MH figures that he must have left his body to do that travelling.
There are far too many amazing things that happen and that are experienced on this Earth that are not explained in the Bible. We are far greater than we appear to be here on this planet. We are not the body; we are the soul.
It is comforting for you to use the Bible as your guiding light on your life's journey, but others may not and it does not discount astral travel nor NDE.
Since doctors know almost nothing about health and wellness, I would conjecture that they also know little on the afterlife.
Check out Michael Newton's Journey of Souls, the Monroe Trilogy or any of the many books on this subject. Keep an open mind and you may be very surprised, yet delighted by what you find.