At the minimum you need four pins: FTDI’s 5V to +5V, TX to ERX (ERX stands for ESP8266’s RX pin), RX to ETX, and GND to GND. GP0 (GPIO0) and RST are for the auto-reset circuit, which you don’t need. Auto-reset allows the controller to automatically enter programming mode based on signal sequence from FTDI, but without the auto-reset, you can still manually enter programming mode by pressing the second pushbutton (B2) while plugging in power. That will tell ESP8266 to enter programming mode.
If you want you can send a support ticket at support.opensprinkler.com and arrange to get a programmer like this one:
https://rayshobby.net/wordpress/wp-content/uploads/2021/10/ch340_cardedge_programmer.jpg
it can plug directly into the PCB edge connector so it’s easier than soldering wires onto the programming pins.
In the firmware, turning on the #define ENABLE_DEBUG at the beginning of defines.h will enable all the debug functions. You can also add additional debug functions. The firmware doesn’t use gdb — when debugging we just use the debug output to check variable values.