What is the most damage possible in Minecraft using a melee weapon?
Sharpness V on a Netherite axe hitting a critical hit deals 18 damage.
If you'd like to count fire damage you could use a Netherite sword with sharpness V and Fire Aspect II for critical hit damage of 15 and total damage after the burn damage of 22. (Fire Aspect II does total damage of 7)
In the Bedrock version, it's a Netherite sword with sharpness hitting a critical hit for 22.875 damage. + Fire Aspect to a total of 29.875 damage.
You can find the different damage bonuses on Sharpness, which applies to any mob: https://minecraft.gamepedia.com/Sharpness