Consider that you are trying to invent within the rules a difference ebtween "take an attack action" and "making an attack" to allow other stuff to be done ***between those*** and my suspicion is that there are likely a broader problem with that kind of logic scope-wise than just this one aspect.
But first lets look at the attack action rules
"With this action, you make one melee or ranged attack. See the "Making an Attack" section for the rules that govern attacks.
Certain features, such as the Extra Attack feature of the fighter, allow you to make more than one attack with this action."
There is no difference in that rule between "taking an attack action" and "making an attack"... making an attack is what the action does. it requires a lot to try and read the Attack action and then see it as not meaning "make an attack" when you take the action.
See, that makes sense, in isolation. If 'taking the Attack action' IS synonymous with 'executing the weapon attack allowed by the Attack action', then a creature with one attack declares/actually attacks simultaneously. That makes sense.
But, if this IS the rule, then it is unavoidable that if the Attack action allows you to execute two attacks (because Extra Attack) then 'declaring the Attack action' and 'executing BOTH attacks' are one and the same thing!
It means that IF the interpretation is that declaring/attacking are the same thing, then BOTH attacks MUST be resolved instantly!
The ONLY way that you can attack/move/draw another weapon/attack someone else 30 feet away later in the round is under the interpretation that 'declaring the Attack action' is NOT one and the same thing as actually 'executing the attacks allowed by the Attack action'!
As JC stated in part of his comments on the subject, the fact that movement between attacks is explicitly allowed does not equate to a universal allowance to insert any bonus action in the middle of the attack action or any action.
The text makes it clear that taking an attack action means making an attack they are not different things that happen at different times.
Since Extra Attacks do not have to be taken all at the same time, and the fact that BOTH attacks must 'happen at the same time' as taking the Attack action, his quote is nonsense.
Also, his sudden insistence that any action, including the Attack action, is 'indivisible', is given the lie by....well...the many, many things in the game which literally can and do occur
during other Actions, including (but not limited to): Readied actions, bonus actions that are not triggered by things that happen in a specific order, free object interactions, as well as movement.
Even in this new 'indivisible' interpretation, the Ftr 5/Wiz 3 can move, 'declare' his Attack action (but only ONE of his two attacks 'happen at the same time'!), shoot an arrow, drop his bow, move, draw his sword, cast
misty step as a bonus action, move, and then complete his so-called 'indivisible' Attack action by executing his second attack.
Yeah, his cries of "Actions are indivisible!" as the
reason that you have to complete your action before you can shield bash are not credible.