In terms of naming / identifying this, do you think it would help to distinguish what makes you want to double down on the current solution? I can think of at least 3 reasons:
Do these all fall within the phenomenon you're trying to describe?
Weather reminder: It will be around 55F on Monday evening, so please dress warmly! And if you have an extra sweater or jacket on hand, consider bringing it to lend to a fellow attendee who finds themselves underdressed.
I've heard some people describe the unnaturalness of the pomodoro method as a benefit. The reasoning is that if you take breaks when you feel like it, you're likely to do it 1) after completing a task and before starting the next one, or 2) when the task you're on becomes unusually unpleasant. This timing makes it more difficult / painful to get moving again after the break. If you instead take breaks when you're interrupted by a timer, there's an obvious point at which to resume and a flow to get back into. You might even want to get back to what you were doing. I've found this somewhat true for myself.
The downside to this approach is that you're more likely to lose a lot of state than if you take breaks at times that feel natural. I don't know if there's a good way to combine the two.