In my experience bad eggs sing “I want it now” before you throw them down the garbage chute.
That guideline seems to be somewhat true in my experience: I’ve never had a new egg that floats, while older eggs are more likely to do so. Also, “middle aged” eggs will sort of float, but not burst straight to the surface. All this tells you is which ones in a mixed batch are older and should be eaten first. If an egg starts to float, it probably has weeks before it indeed goes “bad,” i.e. rotten, so in that sense it’s not a test for bad eggs. No, I’ve never gotten an actually bad one unless it was obviously cracked or something.
I suspect the ones that float do so because they have lost water content thru evaporation thru the porous shell, which is then replaced by air. No indication that it’s bad, just that it’s not fresh.
As an egg gets older the air cell does indeed get bigger. The size of the air cell determines the grade of the egg (AA, A, B, etc). Although my boss always said there is no such thing as a grade AA egg.