The sea soil is tested from time to time as it's a commercial operation. Apparently, the invisible beasties that like to compost the seaweed also break down the things that would become toxic if burnt.
I read a paper on the chemistry about 25 years ago. The temperature the seaweed is broken down has a big influence. It either needs to be fairly cool like a hot compost pile or extremely hot, and then it's gassified and the gas needs to be captured and somethingsomething it was an extremely boring paper even if the topic was interesting. Perhaps science has discovered new things now.
All i know for certain
1. Sea soil is the only soil amendment that I found worth the cost of importing to the farm. It works. I've used it in the garden since the 1990s without any problems. Family has used variations of it since the late 1950s without issue. Composted seaweed is a common historical soil amendment.
2. Biochar is lovely, but in my tests, doesn't show enough benifits for me to spend money on again. I might make some at home, but there is plently of dry material to collect that doesn't risk offing toxic gas when heated. I also feel a bit uncomfortable with the fuel used to heat the char in an industrial setting.