I don’t know where you’re getting the idea that “bacteria aren’t claasified as species”.

They definitely, definitely are. That “coli” in “E. coli” is its specific name.

Streptococcus mutans, for example, the oral bacteria that metabolizes sugar into lactic acid causing dental carries, is kingdom Bacillati, phylum Bacillota, class Bacilli, order Lactobacillales, family Streptococcaceae, and then obviously genus Streptococcus and species S. mutans.