Yes it's definitely an ESP32 chip.
You can use a raspberry pi but the rest way is to get a USB TTL flasher. You can find them for stupid cheap but I like this one as it's well-made and it has activity LEDs that help confirm you've made a good connection. Plus it can toggle between 3.3v and 5v and has a few other nice extras that aren't really relevant here.
The pins on the top left of your photo are actually the ones you want, labeled DBG TX and DBG RX (and the 3.3v and GND)
Should be really easy to flash actually, they did a good job labeling everything and placing it in easily accessible locations. Just remember that the TX pin on the flasher goes to the RX pin on the relay and vice versa.
As mentioned by others the one thing you'll have to look around for is GPIO0 so you can short it to ground/pull it down when turning on/plugging in the device to put it in debugging mode so it will accept a flag from the TTL flasher/raspberry pi.
A good first step would be to try any buttons there might be on the device, often holding the button during startup will work as well. Though having buttons is probably not super common on these relays, a reset button or something like that would have a good chance of working.