“spirulina is a cyanobacteria. Cyanobacteria have traditionally been classified as algae, referenced as cyanophytes or blue-green algae, but today some treatises exclude them from algae.”
The spirulina supplement that’s sold isn’t viable organisms, just “biomass” from dead organisms, so it’s not a probiotic that could compete with gut microorganisms. Nevertheless, spirulina has been studied in IBD and showed some benefit in a mouse model of UC.