It is "during the turn", not "during the action". Moving between attacks is about
movement, not attacks. It is about breaking up your movement, not breaking up your attacks. Why do you think it is under the section on Movement and Position?
A player is not "casting half a spell". Until the action is taken, it isn't taken. That is why you cannot Shield Master shove as a bonus action prior to making an attack.
You keep claiming that because something isn't written in the book, it cannot be done.
You say there is a general rule is stated someplace,
show me where! Where does it say, anyplace, that an action must be completed before another action can be taken? What is written about moving between attacks is further explaination about breaking up your movement.
So, until you show me where it is explicitly written you cannot take one action when you take another, there IS NO GENERAL RULE. Such a "RAW" does not exist. As I have said, repeatedly, neither rule is explicitly written so cannot be considered RAW and it us up to each group to run it as they choose.
As far as bonus actions:
View attachment 345472
You choose when to take a bonus action, including during your action.
Consider TWF. A PC is holding a magical shortsword and a light hammer. He is fighting a vampire spawn and a skeleton. He takes the Attack action on his turn. This allows him to make an attack with the magical shortsword against the vampire spawn. He has taken the Attack action, it is what he is doing on his turn. But he misses! The player decides he should take out the skeleton first so they (hopefully) won't be able to flank him. He then uses his bonus action to attack with his light hammer, reserving the final Extra Attack for his magical shortsword. This way, if he gets luck and destroys the skeleton with the light hammer, he can use the more effective magical shortsword against the vampire spawn. But, if he fails to destroy the skeleton with the light hammer, he can use the shortsword against it, hopefully to finish it off before their turns.