Asgorath
Explorer
Dread Ambusher is not really comparable to Martial Arts or Shield Master, because the extra attack doesn't consume a bonus action. It is just like Extra Attack, but only on the first round of combat.
I think it is important to consider the role of Actions and Bonus Actions in 5e. Neither of them are discrete packets of activity that you queue up, though they might include activities like attacks or spells that are discrete packets of activity. Rather, an Action or Bonus action exist to limit the activity on your turn. When you take an Action, you can't take one of the other Actions. When something uses your Bonus Action, you cannot then do something else that uses your Bonus Action. They represent opportunity cost.
The only unit of time that matters for actions in combat is your turn. Your Action and Bonus Action (assuming you have one) both take place at the same time: on your turn. Individual activities, like actual movement, weapon attacks, spells, flourishes, interactions, etc. all take place in the order the player wants, but the distinction is that those things all have a narrative presence, a reality in the fiction of the game world. Your Action and Bonus Action do not--they are formal constructs of the game system with no objective reality in the narrative fiction of the game world. In other words, you may move 10 feet and make a melee attack, then disengage (as a cunning action) and move another 20 feet. Those are all activities that occur in a sequence, and the timing of them matters. Stepping back to the meta-game, however, you took the Attack Action and your Bonus Action on your turn.
Reactions are different. A Reaction happens in a single moment, triggered by an activity with objective reality in the game world's fiction, and involves the reactor doing an activity with similar objective reality.
But the language of Dread Ambusher is quite explicit that it's giving you an extra attack as part of your Attack action. If bonus actions like Shield Master or TWF acted like this, shouldn't they use the same language?
On your turn, you have an action and your move. The bonus action rules are quite clear that something has to grant you a bonus action before you take take it:
"You can take a bonus action only when a special ability, spell, or other feature of the game states that you can do something as a bonus action. You otherwise don't have a bonus action to take."
Going back to my earlier question, what's an example of a bonus action that has a timing requirement using your definition of bonus action timing? The examples I've been using have triggers that must be satisfied before you can even take the bonus action. The Rogue's Cunning Action is an example of a bonus action with no timing requirement. Shield Master and TWF are ones that have a trigger in the standard form of "If X, Y", and thus the trigger must be satisfied before you can even take the bonus action. Using your "formal constructs" example, you might move 10 feet and make a melee attack, and since the trigger of the Attack action has occurred, move another 10 feet and use your Shield Master bonus action to shove someone with your shield. As you pointed out, the sequence and timing of all of this is extremely important, because until you actually make an attack, you don't have a bonus action from the Shield Master feat. Right? I'm really not following your suggestion that you can just do extra stuff as part of your attack action from features like Shield Master, TWF, Martial Arts and so on. We have examples of class features that do that (e.g. Dread Ambusher) and the language of those does not match the bonus actions granted by Shield Master, TWF or Martial Arts. Fundamentally, 5E is a turn-based game, which pretty heavily implies the ordering of operations is important, right?
So yeah, let's take a step back: what's an example of a bonus action that has a timing requirement? The bonus action rules talk about those, so they must exist in the rules somewhere.