378km in 16.5 hours? That's actually pretty tight. As comparison, for randonneuring 300km brevets are 20h and 400km brevets are 27h. Depending on how fast you can ride at moderate (e.g. zone 3) pace, time management during stops (for food, rest, refills, toilet break, etc) will be an important factor.

Since it is a supported ride, you probably don't have to worry about carrying much, just bring your usual tools and spare tubes/CO2/etc. Maybe extra spare tubes if you're using non-tubeless clinchers, and if the weather looks iffy, maybe a compact, foldable rain jacket. Spare socks if it pours early into the ride. Maybe a gilet or similar if it gets cold where you ride. But remember to bring lights and expect a bit of night riding though (at 16.5h, probably not much but just in case).

Also if possible get to know the route, even if it is a supported ride you may want to be aware of any nearby conveniences (gas stations, 24-hour stores, etc) in case you get lost, support car goes missing, or whatever.