Double Pole GFCI - Pool Rewire - 120V trips GFCI
The GFCI breaker is working as designed. As far as it can see, with neutral run directly to the neutral bar, there is a massive fault that might be trying to kill a person, so it trips.
If you want to feed 120V loads from that breaker you must connect its pigtail to the neutral bar and connect the load neutral wire to the load neutral terminal on the breaker. That way the breaker will be able to see all power coming and going and only trip on actual faults.