I think it is repairable.
I got my 16-35 II fixed after it broke out a piece of an marmot table and hat a nearly fixed zoom ring.
They exchanges the part where yours is broke. The part was bent and zooming was possible but just with quite a bit off force and impossible with one finger like it should.
It costed me about 140€
For your repair there may be some more time and some more parts needed, so expect a higher price tag.