Did you cut the trace connecting SDA to ESP32 Pin-16/GPIO46? I am able to flash my ESP32 with SDA connected to ESP32 Pin-15/GPIO3 (and disconnected from ESP32 Pin-16/GPIO46). Using ESP-Prog I don't have to press the boot or reset button to program.
I suppose using Pin-15/GPIO3 is not the best idea, because like you said it is one of the strapping pins. GPIO3 strapping changes the JTAG source. Not sure yet what effect this has. On the next rev I'll make sure not to use a strapping pin for I2C!
Yea, i did cut the trace connecting SDA to ESP32-S3 Pin-16/GPIO46 and was able to flash it without pressing any buttons. But when i connected the pull-up resistor R19 to ESP32-S3 Pin-15/GPIO3 , i could not flash it. Using ESP32-S3 Pins 4 to 8 or Pin 10 might work to connect to SDA.