1. The bluetti contains a LFP battery which is a higher voltage than lead acid batteries. This can cause the bluetti to discharge into the TV electrical
system. I wouldn't recommend leaving it connected while towing unless you have a isolated DC-DC converter.
2. If the trailer has electric brakes
the emergency braking system needs a source of power to actuate the brakes
and stop the trailer if it becomes disconnected from the TV. This can come from the trailer house battery of from a dedicated battery. Maybe someone will chime in here that knows the Scamp system.
3. The Bluetti has a feature that turns the output off if the output load is less than 50 watts for 4 hours. This is unacceptable for use as a battery for the emergency braking system.
That being said:
1. If the trailer is not equipped with electric brakes
then, connect it where the original battery was connected, and make sure it is not connected to the TV electrical
2. If the trailer has electric brakes than install a trailer braking battery and disconnect the Bluetti when towing.
3. Forget the Bluetti and just install a LFP and charger and don't connect it to the TV electrical
system, or connect it to the TV electrical system thru a isolated DC-DC converter.