While monitoring PSA or PSA doubling time is easy enough, some patients will have tumor progression despite normal PSA and DTPSA.
It would seem that both MRI and CT scan might pick up enlarged lymph nodes and perhaps bone mets, the X-ray exposure with CT offers little return benefit. The question is whether PSMA PET (not Axumin which is less sensitive) will be used only after PSA rises, for diagnostic staging in new patients or for post treatment monitoring.
I've seen some MDs use CEA, CA19-9, CA15-3 and CA125 as part of the monitoring regime. Whether liquid biopsies will be helpful is also unclear. While tumor markers such as urinary micro RNA for initial prediction of a cancer diagnosis, microsatellite instability and tumor burden have been useful in endometrial, GI and melanoma to predict immunotherapy benefit they don't seem to be helpful for prostate cancer.