Already in ancient times, all life on Earth was classified into two "kingdoms": plants and animals. This division remained in place until relatively modern times, including in Linnaeus's work. By the mid-20th century, life was typically divided into five "kingdoms": prokaryotic life (bacteria, etc.), animals, plants, fungi, and protists. However, recent research has shown that "protists" is merely a catch-all category for eukaryotic organisms that are neither plants, animals, nor fungi. Some protists are more closely related to animals and fungi, while others are closer to plants, and some are not closely related to any of these groups. Today, the classification of life is far more complex than the traditional "kingdom" system.
Now, to my question: Historically, many organisms have been classified under the name "algae." Roughly speaking, any organism capable of photosynthesis that was not a land plant was grouped under this term. Traditionally, all such organisms were placed in the plant kingdom. However, we now know that while some, such as green and red algae, are indeed closely related to plants (in fact, "green algae" is now recognized as paraphyletic since plants evolved from them), others, like brown algae, are not, and belong to entirely different branches of the tree of life. While this has been confirmed through molecular genetic studies, I believe it was recognized earlier that certain groups, such as brown algae, possess distinctive features that set them apart from plants.
Historically, when was it first recognized that some groups of algae, such as brown algae, are not closely related to plants? Can anyone provide insights into the timeline and development of algae classification outside the plant kingdom?