There is no blood test that can definitively diagnose psoriasis
(UpToDate).
The article linked from the question (Arthritis.org) mentions several studies; in one of them uric acid was elevated in only 20 percent of patients with psoriasis. In another study, it was psoriatic arthritis that was most strongly associated with elevated uric acid. So, it may not be the severity of psoriasis, but rather the type of psoriasis and the presence of arthritis that affects the uric acid levels.
According to this 2015 article Biomarkers of An Autoimmune Skin Disease—Psoriasis, the following biomarkers (which are not usually checked in a diagnostic process) can be elevated in psoriasis:
- Nonspecific inflammation markers: C-reactive protein (CRP), platelet P-selectin, haptoglobin, complement component 3 (C3), and C4
- Pro-inflammatory cytokines: TNF-α, IFN-γ, IL-6, IL-8, IL-12, and IL-18
- Markers of abnormalities in blood fibrinolysis and coagulation: increased levels of fibrinopeptide A, fibrinogen, D-dimer, and C4, in addition to decreased levels of protein C, alpha 2-antiplasmin, and plasminogen