It doesn't look like cancer.
"Clinical correlation suggested" means that the blood smear results don't point to anything specific, so you have to look at history and symptoms to make a guess. Meta, myelo and promyelocytes are just stages of immaturity - pro being earliest.
Everything becomes a matter of probabilities.
Medical sites often talk about possible cancer first, because that is most serious; but it doesn't mean cancer is the most likely. The smear (with microscope) didn't happen to see any leukemia cells. Besides, overall: cancer doesn't really fit, else the docs would be doing flow cytometry or marrow biopsy.
Another cause is some bacteria/fungal infection, but you don't have fever or elevated neutrophils. A virus would more likely be causing immature lymphocytes, not granulocytes/neuts.
Another possible cause is some autoimmunity, but that doesn't fit everything. You'd likely had ANA tested just as a matter of course, right?
Then there is some non-cancer marrow dysfunction, which isn't likely but is left when other possible causes are even less likely. That'd want a marrow biopsy, to look for fibrosis and inflammatory cells or anything odd. But the marrow probably wouldn't cause generalized lymphadenopthy.
If you really fear cancer, you can push for ultrasound of the most suspicious node(s). Though my guess is none are genuinely suspicious anyway and they instead seem reactive (not cancer).
So what is ultimately left is some mystery inflammatory process. Maybe non-infectious. Maybe part of ANA-negative Lupus. Or maybe Lyme or similar, which can do many mysterious things.