ezo
Hero
Firstly, this is about breaking up movement, not your action. It has nothing to do with action, other than you can move incrementally before or after, and in the cast of Attacks, inbetween. This is done solely to illustrate that when attacking, you are permitted to move inbetween attacks by default. Nothing stated even implies prohibiting other actions during the Attack action. It is entirely up to the DM.
It is also important to realize that things "in the game" are not happening in static "stop/start" motions.
Consider an example of a PC with sword drawn running to engage a foe, his other hand is empty.
1. I move 5 feet to be within 20 feet so I can throw the dagger without disadvantage due to the range.
2. Drawing the dagger as a free object interaction, I throw the dagger using my Attack action.
3. I move 20 feet to engage the target in melee.
4. I attack with my sword using Extra Attack.
The second part of the "action" doesn't mean my PC actually "stops" to throw, but is more likely the throw is done as I am moving.