The Clinically Important List of Urease Producing Bacteria
The bacteria you mentioned are important microbiologically in other words important for Step 1.
But for Step 2 CK there are other urease producing bugs that are far more important clinically.
These are:
Staphylococcus, Klebsiella, Pseudomonas, and Providencia.
Important UTI bugs that absolutely does not produce urease are E.coli and Streptococci and Enterococci.