An unfortunate thing about the breadboard-style ESP32 adapters is that most of them don't include any bulk capacitor at all, and the ESP modules themselves don't incorporate bulk capacitors. ESP32s are very "bursty" in their power usage, mostly due to WiFi. As a result, it can be hard to make them work reliably in these kinds of breadboard setups.
In addition to the large electrolytic on the breadboard power rail (which is probably quite high ESR), I'd recommend adding a low ESR electrolytic, or a tantalum or ceramic capacitor with a reasonable capacitance (10uF+). Put them as close to the module as possible, try to minimise the breadboard wires or breadboard traces in the current path. Soldering to the module itself would be the best!
@Ken_Taylor, if your sometimes-glitching module is also this type then it may be worth trying the same things.
(The other alternative, now that third party dev boards like the one @Harvs posted are on the market, is to switch to these. All the designs I've seen include an on-PCB bulk capacitor.)