what happens if we connected a motor or a 3 phase tool to the 380v plug? (the output with only 2 phases connected.)
It would never be wired to a 3 phase output from 2 phases, but if it were , the motor would not run and would overheat.
It is very common to create single-phase higher voltage from two Line-to-Line phases to meet equipment requirements. The 1st 3 breakers on the left share 2 sequential phases e.g. AB BC CA with double pole breakers. This is the proper way to distribute 3 single phases at the higher line to line voltage. If all 3 breakers were loaded roughly the same , then the power source would see balanced loads. It is up to the electrician to ensure these loads are fairly well balanced.
The next breaker has all 3 lines + neutral ganged through breakers.
If you have a logic diagram to show what you think is wrong use the schematic tool or draw it.