Welcome, Finny!
I had a very similar problem several times a month recently, with damp adhesive after the first day and climbing blood sugars that seemed unaffected by repeated corrections, and with the cannula and adhesive firmly in place. Then I read about tunneling, a situation that happens mostly with Teflon cannulas in which the insulin backs up along the cannula to the surface.
I noticed the leaks were more of a problem when I gave larger boluses, so I started to reduce the amount of bolus I gave at any one time (and on the Omnipod, extend the remainder over half an hour). I started with 9 or 10 and worked down, and I’ve found 4.5 to 5 U is safe for me. I haven’t had any back-up leaks since then. You might give this a try. It’s a bit of a nuisance, but not as much of a nuisance as climbing highs and corrections that do nothing!
Another minor nuisance is that if you tell the PDM to deliver, say, 5 U, it may decide to give you more: see PDM fails at math? for the explanation. Good luck!