ESP32 stalls b/c of current spike (inrush current) - how to limit inrush current?
I'm looking to replace that with an LV78S05CV, which can handle 2A.

Instead of replacing the original regulator, add another one to power the problematic 'component'. This keeps the surge current away from the original regulator, which then only has to handle voltage sag on its input. A 78M05 wiould be a good choice for the second regulator because it limits current to ~0.8 amps maximum.
If your power supply can deliver this current without sagging below 7 V the regulator powering the ESP32 should have no trouble maintaining a stable output when the 'component' is switched on.
If your power supply can't handle the surge current without dropping below 7 V then you can can add a diode and capacitor to the ESP32 regulator input to hold its input voltage up during the sag. The circuit looks like this:-



simulate this circuit &ndash; Schematic created using CircuitLab
Diode D1 prevents the 'component' from drawing current out of reservoir capacitor C1 when the power supply voltage sags.
Use a high current Schottky diode for lowest voltage drop (important because the 7805 has a 'dropout' voltage of ~2 V). Using an LDO (low dropout) regulator such as the L4941 to power the ESP32 could also help, as the reservoir capacitor can then discharge a bit more before the regulator drops out of regulation.