Considerations for debounced power switch with Li-ion battery source
Switches can have surprisingly low current rating. Check the switch datasheet. Furthermore, the current in-rush to charge capacitors when the switch makes contact can age the switch prematurely. (I don't know if this is a risk at 5 V.)
Using just a capacitor to debounce the signal relies on the resistance of the power source, wires and capacitor to limit the turn-on current and signal rise time.

A safer approach to all this is to use the switch to control a transistor or IC switch (such as TPS22919) which in turn powers the regulators, or to control the regulator(s) enable pin if such exist. Then add a resistor to the switch output to form a RC network with your capacitor (which can now be much smaller). There are many online tools to calculate the values for resistor and capacitor to fit your debouncing time, for example https://www.digikey.com/en/resources/conversion-calculators/conversion-calculator-time-constant

EDIT: To get 5 V from a single-cell Li-ion cell (3.3 - 4.2 V), you can use for example this: https://www.pololu.com/product/2123
It has an enable pin, which you can drive with your switch (and RC network).