Short answer
Use the date, storage history and shell condition, then crack the egg into a separate bowl. Discard leaking, slimy, badly damaged or offensively smelling eggs. No home test can prove an egg is free from pathogens.
Freshness is not the same as safety
As an egg ages, the air cell grows, the white thins and the yolk flattens. These are quality changes. Salmonella can be present in a clean-looking egg, so appearance and smell cannot replace proper sourcing, storage and cooking.
What the float test shows
An older egg contains a larger air cell and may stand upright or float. That makes the test a rough indicator of age, not contamination. A floating egg is not automatically spoiled, and a sinking one is not guaranteed safe.
A sensible checking sequence
Confirm the relevant carton date and whether the egg stayed at the required temperature. Check for cracks or leakage. Crack each uncertain egg into its own clean bowl so an off odour or unusual appearance does not contaminate the other ingredients.