Green algae are still considered in Plantae, Charophyceans/Coleocheteae
are very plant like and have differentiated cells, in many ways so do
Caulperales, kelps etc, they went a different pathway but are extremely
successful and very plant like.

Byrophytes are an odd group as well.

BGA, Cyanophyta/Cyanobacteria (whatever you prefer to call them,
Cyanobacteria works well) are very unlike ANY other group of bacteria,
so much so I'd consider them almost in their own group, they possess
thyalkloids, but not chloroplast. Most folks that do the work on this
group are phycologist, not microbiologist, most of us retain the term
BGA as a common name. Zoo folks call Divisions, phylums and plant folks
call phylums Divisions, depending on what side of the fence you are on.

I did like that you referred to algae as "a type of plant".
Regards,
Tom Barr