D&D is a turn-based system; you can only do stuff on your own turn!
Whatever that 'stuff' is.
Unless you have a specific, written exception.
'Talking' (briefly) is such an exception.
So are Reactions.
But 'dropping something' is not.
JC has not made 'dropping' an item a 'no action'; he simply acknowledges that the use of a two-handed weapon involves the constant shifting of your grip, and that each hand continually releases and re-grasps the weapon as part of its use. Two-handed weapons do not require both hands to be glued to it! You just have to have two hands free (of anything apart from the weapon, obviously) in order to execute an attack with it. When not actually executing an attack, you only need one hand to hold it. Weapons are physically balanced with this in mind.
Note that at any given instant, at least one hand will be gripping the weapon, but it switches from hand to hand, and from 1H to 2H, constantly while being used. But you need two hands available to manipulate it at the moment you execute an attack with it.
But if you want to drop it, whether it is a 1H or 2H weapon, that is something you choose to do. You can only do stuff on your own turn. You cannot choose to drop an item when it isn't your turn.
You can only choose to cast shield when it isn't your turn because Reactions are specific exceptions. You cannot choose to drop an item outside of your own turn.
If you have a weapon in one hand, whether it is a 1H or 2H weapon, then your other hand is free to cast a spell. If you are holding a 2H weapon in one hand while your other hand is free, then you are able to execute an attack with it because you have two hands free (holding nothing but the weapon) at the moment you execute the attack.
If you are holding two weapons or a weapon and a shield, then you do not have a hand free to cast a spell, and you may not choose to drop a weapon when it isn't your turn.
If you TWF or sword & board and want to cast spells, you need the Warcaster feat, or if you can use a holy symbol (and the spell has a material component that doesn't cost money) then you can have the holy symbol on your shield and so you don't need a free hand to cast that spell.