Here is a nice neuroanatomy review.

https://www.ncbi.nlm.nih.gov/books/NBK526119/#article-20094_s1

As others have said a lot of our sensory and motor fibers cross at decussations mostly in the medulla but cranial nerves do not. Cranial nerves do have hemispheric cross over in some cases like using CN3 for example in how eye muscles work. Although you are talking about CN7 for blinking. I encourage you to read the link I posted but for a TLDR;…..

Upper motor neurons for CN7 in the cortex talk to both dorsal and ventral portions of the contralateral facial nucleus in the pons…and the ipsilateral upper motor neuron also gets to talk to the ipsilateral dorsal portion of the facial nucleus….dorsal portion controls muscles of upper face = orbicularis muscle = allows bilateral closure of eyelids….ventral portion of facial nucleus receives innervation mainly from contralateral tracts…which controls muscles of lower face….so contralateral input only is in control of lower face….this explains why in Bell’s palsy which is an idiopathic palsy of a unilateral lower motor neuron you get a total knockout of upper and lower facial muscles….while if the upper motor neuron was the problem you would only have paresis of the contralateral lower face.

Bout as TLDR as i could make it.