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'!
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.