If a player goes to "combat", and then activates an ability, what is the game state?
As of the release of Amonkhet, the &quot;Go to combat&quot; tournament shortcut changed, and it now unambiguously supports Anthony's interpretation of the sequence of events. The game is in the beginning of combat step and Mutavault's ability is on the stack. Noah has priority.
The current wording of that shortcut is

If the active player passes priority with an empty stack during their first main phase, the non-active player is assumed to be acting in beginning of combat unless they are affecting whether a beginning
of combat ability triggers. However, if the non-active player takes no action, the active player has priority at the beginning of combat. Beginning of combat triggered abilities (even ones that target)
may be announced after any non-active player action has resolved.

The Amonkhet policy changes announcement describes the practical impact of the change to this shortcut:

What this does, in a bunch of words, is set the default case so that the active player moving to combat (usually) means that the non-active player is acting in beginning of combat, but the active player’s role there only happens after that. They haven’t missed triggers, and they can still crew. But, by offering to pass priority into combat, they can no longer claim to be in main phase for non-instant spells afterwards unless the non-active player took an action to prevent the trigger.

In the situation in question, activating Mutavault serves the same purpose as the ability to crew that they mention: it turns a non-creature object into a creature in preparation for attacking with it.
In addition, that same blog has a post that takes a more detailed look at the change, and it discusses a scenario that involves actions like those described in the question:

The Cryptic Command Problem
It’s not a problem with the shortcut, per se, but it’s a protection for the non-active player that’s been removed. There are various permutations of the “Phantom Priority Pass”, but here’s a simple one:
The active player has a two Bears and a Mutavault. The non-active player is at 5 life, but active player is worried about a Cryptic Command.
The active player wants to try to get a read on if the coast is clear. So, they say “Combat” in an attempt to imply that they’re ready to declare attackers. If the non-active plays the Cryptic, you activate the Mutavault and get in for 2. If they don’t, unless they’re a very precise player, it’s a strong sign that they may not have it and you should activate the Mutavault and go for it. The old shortcut precluded that baiting.
Of course, the correct time to play the Command if you have it is after the second priority pass (or interrupting the declaration). But now you need to be more careful if you’re the non-active player to not accidentally tip your hand.

The &quot;if they don't [play a Cryptic Command]&quot; scenario plays out exactly like the one in the question: the active player announces that they are moving to Combat, the non-active player takes no action, then the active player activates Mutavault and attacks with it.