They existed, but only very, very late.Probably wrong but I don't think that eliminates the belief that transistors would exist on robots.
Just another classic example of retcons. We do know Eyebots used circuit boards and they were mass produced
Eyebots are a postwar development by the Enclave, makes sense they'd use them.
But Mr Handies are proven to have em as well, and they were a somewhat common household product.