Technically, It’s Still Free
Dropping a weapon counts as unequipping it in the context of an Attack action, but this context is limited to that action:
Equipping and Unequipping Weapons. You can equip or unequip one weapon when you make an attack as part of this action. You can do so either before or after the attack. If you equip a weapon before an attack, you don’t need to use it for that attack. Equipping a weapon includes drawing it from a sheath or picking it up. Unequipping a weapon includes sheathing, stowing, or dropping it.
The inclusion of "dropping" here is part of the definition of "unequipping" in this special context. However, there is almost never a reason to drop something instead of stowing it for free as part of the Attack action, because dropping a weapon risks someone else picking it up. Thus, the Attack action rules provide additional action economy, demonstrating how exceptions supersede general rules:
When an exception and a general rule disagree, the exception wins.
It would be imbalanced and illogical to treat dropping a weapon as equivalent to actions like opening a door, pulling a lever, or sheathing a weapon. The latter actions demand time, attention, and coordination, while dropping something requires no effort, a fact corroborated by the rules for falling Unconscious:
You have the Incapacitated and Prone conditions, and you drop whatever you’re holding.
This supports the argument that dropping an item is effortless and should not constitute a Time-Limited Object Interaction.1 Otherwise, dropping a weapon would require a different action economy than any other object, even though no rules define the cost of dropping an object, and dropping a weapon is never described as a Time-Limited Object Interaction.
As another user pointed out, dropping a weapon should require no more time or effort than removing one hand from a Versatile:
A Versatile weapon can be used with one or two hands.
or Two-Handed weapon:
A Two-Handed weapon requires two hands when you attack with it.
The RAW (Rules as Written) do not assign a cost for switching between one-handed and two-handed use of a Versatile weapon or for holding a Two-Handed weapon in one hand. The 2014 PHB originally described the Two-Handed property as:
Two-Handed. This weapon requires two hands to use.
(cited here). This was clarified in the errata:
Two-Handed (p. 147). This property is relevant only when you attack with the weapon, not when you simply hold it.
The 2024 rules now explicitly state:
...when you attack with it.
This implies that holding a Two-Handed weapon in one hand is valid. Since no cost is defined for switching between hands or grips, it is eminently reasonable to infer that these actions are free.
By tying the unequipping rule specifically to the Attack action, the game avoids unnecessary complications in action economy while maintaining consistency. Treating dropping a weapon as anything other than free would create conceptual absurdities and undermine balance, forcing players to spend disproportionate resources on a fundamentally effortless act. This design choice ensures mechanics remain intuitive and balanced while preserving the intended fluidity and strategic depth of the game.
Addendum:
This question was updated to address dual-wielding. The assumption that dropping a weapon requires expenditure of the free environmental Interaction implies that a character cannot drop two weapons and take an action (other than Attack) in the same turn. This interpretation becomes even more problematic when considering the Dual Wielder feat, which allows stowing two weapons simultaneously but does not explicitly address "unequipping." Such a restriction would be inconsistent and absurd.
1: The designers assumed this in 2015: ...letting go of something requires no appreciable effort. But picking it up does.