I always take my phone with me for music but also for emergencies. I make sure any running shorts I buy have a pocket at the back to keep the phone in (like these). A pocket here tends to hold the phone tight and distributes the weight evenly so I just forget it's there really. Other people like the flip belt or the naked running band for holding phones but I find these can get a bit hot/annoying.
Do you not find that the phone bounces around everywhere? That's one of the reasons I stopped too!
Can't beat short shorts for racing/workouts. My pixel 6 is very large and just fits into those shorts pockets although at 6.4 inches is probably the limit. The pockets are stretchy, except for the zip obviously, so can adjust to suit what size phone you have.