What is the purpose of the twin single pole breaker?
Some things don't need common trip, they just common maintenance shut off. A 2 pole breaker provides both these things but not everything needs that.

The white things are called handle ties. You wouldn't expect to find them on every breaker, just the ones that need common maintenance shut off.

The two Breakers in one space are exactly what it says on the tin. They are separate Breakers with separate trip. I have never seen double stuff Breakers with handle ties, but if the manufacturer supports it then okay.

One thing that does need common trip is the pump. That should not be on a double stuff with handle tie. That should be on a 2 pole breaker. Now they do make quadplex Breakers which are two double-stuffs with a proper two-pole breaker in the middle; all that will fit into 2 spaces. That is what they should have used in that location.

I certainly hope that you tested the bathroom receptacles to see if they already had GFCI protection before installing a GFCI receptacle for no reason. Putting a GFCI on a GFCI is a waste of money. None of the breakers in that panel are GFCI Breakers, in fact there's no such thing as a GFCI double stuff.