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Seeking advice after tire repair

2022 MYP with 21" Michelin Pilot Sport tires. Current milage approximately 13,000 miles. Had a nail in rear wheel at the end of last summer (around 8500 miles)
I had it patched and plugged while the winter wheels were on. The guy who did the repair had to do the patching twice because it "did not stick" the first time. In fact, he sounded suspicious that it would not work.
Anyway, I kept an eye on it during the winter while it was off the vehicle. No problems. I put it back on in April and it held very well...until now. I can detect a very slow leak (1 PSI every 2-3 weeks); so it is not an emergency. However, I am concerned that it would get worse next year.
My Question: I am thinking of using the sealant sold by T Sportline, which is safe for these tires. My rationale is that this would seal a possible tiny leak around the patch and would save me from replacing the tire (and the possibly the other tires) for at least one more season. Does this make sense?
Would you do this? If not what is the drawback, other than losing a few $.
If the leak is around the patch, have the same shop try to fix or possibly take it to another shop to evaluate and see if they can fix. I've had similar probably where one shop tried multiple times to patch, but failed but another shop fixed it right the first time. I feel like sealant are for emergency situation to get you safely to your destination or a tire shop and not as a permanent solution.