Twitter is not a neologism, but a word in the english dictionary: https://www.merriam-webster.com/dictionary/twitter ("to utter successive chirping noises"). As is tweet: https://www.merriam-webster.com/dictionary/tweet ("a chirping note").
My knowledge of trademark law is limited, but I guess if someone would like to sell "Twitter"-sausages, they would have to apply for that trademark in the respective category and it could be anyone, as the-company-formerly-known-as-twitter propably doesn't have the trademark for food?
As I understand it, some brands are strong enough and globally-applicable enough that you can't use them regardless of what you're trading in. If you were to sell "Nike sausages," I'm pretty sure you would get sued and lose in court. Other times, the brand is more limited and you can get away with re-using it.
As a slight counterpoint, Bells Labs was selling Nike Missiles before the shoe company ever existed. I imagine that they’d be in a good place legally to continue that brand name.
