Example circuits for minimal power upon waking up in RP2040 microcontroller present in this app note from Raspberry Pi. Link here (PDF)
Even in deep sleep RP2040 draws a typical current of ~180μA, and sleep current is very dependent on PVT: process (current varies from chip to chip), voltage (current varies linearly with voltage), and temperature (current varies nonlinearly with temperature).
For many use cases where minimal current draw is required, the best option is to power off the system (or the RP2040 part of the system) completely if possible. This application note gives a couple of options for how this can be done, and these circuits are simple enough that a designer can adjust them for their own use case.