Electrical – a good circuit design to drive this relay safely from an ESP32

The switch is getting stuck because of the surges of current that the capacitor draws. Each time the switch closes, the capacitor looks like a short circuit until it charges up. Without the capacitor, the current was limited by the coil in the relay; with it, it is limited only by the ESR of the capacitor.

One possible way to mitigate this in the short term would be to add a resistor in series with the switch. Select a value that doesn't cause more than, say, 0.5V drop with the coil alone. This will provide an upper limit on the surge that the capacitor can draw.

A better long-term solution would be to eliminate the capacitor altogether and instead use a different kind of float switch that has a hysteresis effect. With this kind of switch, the pump turns on at one (higher) water level, but turns off at a different (lower) level. This is how most sump pumps work.

This effect can be simulated by using two float switches of the type you have, plus an auxiliary relay.

To elaborate on Peter Bennett's answer, here is the standard relay driver circuit I use. It removes the requirement that the 555 can supply the full current of the relay.

^{simulate this circuit – Schematic created using CircuitLab}

Notes:

• Relay power doesn't have to be the same power supply as the rest of the logic, but it can be if that is adequate voltage for the relay. Ensure the relay power supply voltage is adequate to close the relay.
• Select Q1 for adequate relay drive current. For large relays, the 3904 may not be appropriate. Also ensure that the device will saturate. A darlington connection may be required for very large currents.
• D1 is a flyback diode required to protect Q1 from voltage spikes caused by the relay coil.