A couple links with articles for consideration.

With USPSA, we can be focused on the PSA vice the standard PSA tests, measuring only to a single decimal. Your labs do show a continuous rise though there is debate about calculating doubling and velocity times with USPSA. Still, valid concerns with those increases.

The sensitivity of the newer scans below .5 does not mean it can't locate the PCA, just that as PSA hits .5 or higher, that sensitivity increases. Your decision, does waiting for PSA to hit .5 or higher and increase the sensitivity in locating the PCa change the outcome, i.e, does the treatment plan change if you wait and increase your chance of locating the recurrence. Perhaps not. If you have the financial wherewithal, that enters the equation too. If you're battling with insurance companies, well, that's a factor we know all too well.

When dealing with insurance companies, I find it useful to cite the NCCN guidelines https://www.urologytimes.com/view/psma-pet-imaging-modalities-added-to-nccn-guidelines-for-prostate-cancer. Medicare follows these are they are the "standard of care."

To sum up:

Your sustained increase in PSA as evidenced by your USPA results may clinically indicate recurrence.
The decision to image may want to take into account the tradeoff off between sensitivity, the impact on the treatment plan and any risk associated with a higher PSA, thus greater sensitivity to locating the recurrence and informing the treatment plan, particularly if you are considering radiation to any sites located by the scan. If radiation were not in play, just systemic treatment, that may change your decision process.
https://www.prostatecancer.news/2016/12/pet-scans-for-prostate-cancer.html
https://www.prostatecancer.news/2020/07/the-perils-and-pitfalls-of-treating-psa.html