I too was on June security patch. Read neopolotin75's reply (2nd above) and thought to give it a try. But, only extra sim I had was a Tello, T-Mobile MVNO. Put Tello sim in my Note 20 Ultra 5g Factory unlocked from Samsung and when phone powered up I had the July update waiting to download. Download finished and installed, phone rebooted and August update available. Downloaded and installed, all working well with Tello sim.
Put T-Mobile Sim back in, August update showing in settings and everything working fine. That's insane, phone wouldn't update with T-Mobile sim which I was using from day one but updates with T-Mobile MVNO sim. Go figure?