Is "seafood" inclusive of "seaweed"?

I told Korean friends not to label a (non-commercial) package of seaweed as "seafood", but it is from the sea and it is food, so now I'm not sure.

How common is it to refer to "seaweed" as "seafood"?

Does this vary from place to place?

I wasn't able to find any dictionary which included plant-based food in the definition of "seafood."

Merriam-Webster (American English):

edible marine fish and shellfish

American Heritage:

Edible fish or shellfish from the sea.

Chambers (British):

Shellfish and other edible marine fish.

Some other sources:

• The US FDA has a searchable "seafood list." I did not find any plants in the list, just glancing through it.
• The Wikipedia article includes plant-based food, but the simple version does not.
• The University of Maine's Sea Grant "Seafood Guide" lists seaweed.

So it seems like seaweed can be considered seafood, but it does not seem to be common practice. I would never use the term to refer to seaweed or other plant-based food.

A state of Connecticut definition (for the purpose of a specific law concerning the requirement of a certificate of registration for the retail sale of seafood) is:

"Seafood" means all fresh or saltwater finfish, molluscan shellfish, crustaceans and other forms of aquatic animal life

[emphasis added]

which would lead us to believe that plant products are not included in the category 'seafood'.