According to the rules an action slot ends "once both players have chosen not to take an action"

How strict is this rule? Is it Player A passes, Player B passes => End of the action slot? In this case B would have control over the ending of the slot.

Or can player A at this point take another action, even if both players have passed consecutively before?

No, but say A plays Action, B passes. Now A has "control", if he passes Action window is over.

So it's strict. Two consecutive passes mean the end of the Action slot and we move on to the next phase / sub-phase

Correct. For reference this is explicitly stated in the rule book if you need to prove it to your opponent.