I think your second grouping is correct. As written, the second "and" seems to draw a line between one group and another. Your second grouping seems logical, "plankton, fish and shellfish" are animals poisoned directly by something (red tide?), while "animals and people who eat them" are poisoned at second hand. I think I would leave out the first "and" and put a comma after "shellfish:" "It may also poison plankton, fish, shellfish, and the animals and people who eat them."

Do people eat plankton? Yes and no. They don't eat it directly but they do eat the animals that eat it. Hence your sentence has built-in ambiguity that is best removed: "It may poison plankton. Thereby, fish and shellfish that consume plankton are poisoned as well and the toxic chain extends all the way up to human beings."

it's a complex sentence 1st and unites 2 parts of a complex sentence 2nd and unites two subjects "animals and people"