TLDR: ATC has no way of knowing what frequency you are on, or when you have switched to the next planned controller.

ATC has no way of knowing what frequency you have switched to, but they can infer you had made the switch too early if your next acknowledgment or transmission is on the departure frequency, vice the tower frequency. This assumption could be false, if they just didn’t hear the cancelled take-off. In North America standard airline practice with a clearance to “contact departure airborne” is to -not- switch from tower frequency until at least 1000 feet above ground level. So switching on the take off roll would be completely wrong, almost certainly in Portugal too for this very situation.

More likely though, is the Azul pilots just didn’t hear the cancellation of the take-off clearance. This can be because of poor radios, high density use of the frequency, task saturation or expectation bias. Pilots are people and cleared to take-off is a pretty big clearance to take back, and it happens almost never.

Finally, this situation is foreseen albeit rare. This is one reason why TCAS (collision avoidance) systems exist for aircraft in high density airspace. Errors can occur and in this instance independent transponders on the involved aircraft will have automatically interrogated each other and worked out a solution considering all factors, including proximity to the ground, far faster than ATC can come up with a plan and communicate it. While sub optimal I would suggest that the pilots did a good job correcting the errors that occurred, and the real cause for concern is quite likely the high amount of traffic in one place at one time, likely a controller being asked to cram in too many planes in at once. But that’s just conjecture.