Howdy and sorry that happened.
I know that's frustrating as it's happened to me twice in my decades of cycling and once to my wife on her bike.
All 3 times it was caused by the rear derailer limit screws not dialed in exactly to prevent over shifting.
There are 2 limit screws , usually marked with an L for low or an H for high.
The low one sets the limit of the derailer to not go beyond the big cog of your cassette or freewheel to prevent sending the chain into the spokes.
The high screw prevents the derailer from over shifting to the outer most small cog of the cassette or freewheel to prevent sending the chain off the cassette causing it to get stuck between the cassette and the drop near the derailer hanger possible bending it.
From my experience sending the chain into the spokes is the worst as it can bend or break spokes which will cost even more to repair.
Either direction of an over shift sucks.
It's made be paranoid about double or triple checking when I install a new derailer.
As to dropping a chain into the spokes that's why many bikes come with the so called 'dork' disk that fits between the cassette and spokes.
One bike shop owner/mechanic on YouTube that calls himself the Bike Farmer insists on installing new disks because he's seen that over shift happen so often causing damage.
Two times on my incidents the two bikes had replaceable derailer hangers and it was fairly simple to resolve.
Once my derailer broke in half just like yours.
Another time it wrecked 9 spokes and it was a $60 repair bill to replace and true the wheel.
Perhaps 'dork' disks are not such a bad idea although I don't currently have any on my bikes I do really pay close attention to the derailer limit screws.
I'm sure there are others that can give a better or more precise explanation but maybe that helps some.
I hope you get your Platy back on the road quickly.
I have a similar rear seat on one bike to carry my granddaughter.
Safe riding,
Paul in Dallas
box_liam on Instagram
From the picture it looks like your chain stuck on the outside.