Does the cleanup step use the stack or do effects end without players getting priority?

The cleanup step is specifically designed to wrap up the turn without interruption. Under CR 514.1, the active player discards down to their maximum hand size (normally seven), and under CR 514.2, damage is removed from permanents and 'until end of turn' or 'this turn' effects end — all of this happens simultaneously without using the stack and without players receiving priority.

This means triggered abilities that trigger during cleanup do not immediately go on the stack. CR 514.3 states that if any triggered abilities trigger during the cleanup step (or if any state-based actions need to be performed), players do receive priority once in order to handle those — and then another cleanup step is performed afterward. This is the only exception to the 'no priority' rule in cleanup.

CR 117.3 confirms that players only receive priority when a rule or effect specifically grants it, and the cleanup step does not do so under normal circumstances. This keeps cleanup fast and automatic in the vast majority of games.

Concrete example: Your opponent controls a Runeclaw Bear with a +1/+1 counter and you cast Giant Growth on it during combat, making it 4/4 until end of turn. In the cleanup step, the +1/+1 from Giant Growth expires automatically — no stack, no priority. The bear returns to 3/3 (its base 2/2 plus the counter). No player gets a chance to respond to this effect ending.