This is really at least partially an answer. Clearly foraged foods lived on, but genetics has shown us that pre-agricultural, hunter gatherer Europeans were ver

This is really at least partially an answer. Clearly foraged foods lived on, but genetics has shown us that pre-agricultural, hunter gatherer Europeans were very genetically quite distinct from post-agricultural (and post Indo-European migration) populations, and we know that they were not Indo-European speakers, too. So it's also quite likely their cultures were lost and along with them at least some of the foods they ate. Which is not to say that people living in these places didn't continue to eat seaweed, because they did.