I can't tell you whether or not you should wait and see, but I think I'd ask for some further testing - MRI or ultrasound, and probably a biopsy - then make some decisions.
It's good that your PSA is falling, not rising.
Since you've had recurrent issues with this, I wonder if a doctor has mentioned chronic prostatitis or chronic pelvic pain syndrome to you?
Here's an article on prostate nodules - https://www.healthline.com/health/mens-health/prostate-nodule Many times, they aren't cancer.
My dad had meta prostate cancer, and had it for years before it spread to the bone. His PSAs were much higher than yours - often into the 200s and 300s.
The liver scan probably wouldn't have shown your prostate. The liver is pretty high in the abdomen, and the scan wouldn't have gone far enough to see the prostate. You can ask your doctor if yours did, though.
Let us know what happens.
You should follow the advice of your urologist. If elevated/rising PSA, consider MRI prostate on 3T magnet, not US or CT. CT is only good for evaluating prostate size not prostate lesions. If you see prostate cancer on CT, it is usually so bad it extending out of the prostate and spreading to lymph nodes and/or bones, and you do not want to wait to that point.