I know that I read about some sort of outside the box use for seaweed in the Caribbean which the locals came up with exactly due to the problems you're talking about. I think they were making building blocks out of it!
We love to say in Permaculture "the problem is the solution" and biochar is certainly one option.
One concern I have is getting the seaweed dry enough that the charring is as efficient as possible. Do you do anything special to manage that?
A second concern is that I've heard locally that burning salty wood in a wood stove damages the metal. It sounds from your description that you're burning it in a cone, so that may be less of an issue than a wood stove. How many cycles have you tested your system with, and has there been any sign of damage?
I definitely agree in principle. This is a good option for areas where pollution is an issue.
Some of the other good uses are composting, animal feed, human feed, and some of the suggestions in these links:
https://www.greenislandcreative.com.au/blog/5-uses-for-seaweed
https://earthbound.report/2021/04/15/10-different-uses-for-seaweed/
I find it interesting that the Caribbean and some other places are struggling with an excess of seaweed, and in my region, we're trying to encourage the recovery of our kelp forests. Kelp is a key link to keeping the entire northwest coast ecosystem healthy.