I’ve had several hard cases on my phones, including an Otterbox, but as Cougar says, they’re bulky, the built-in screen protector is garbage, and after a while I binned it and just used a clear silicon case with a glass screen protector.
My current phone, an iPhone 11 Pro Max has a glass screen protector on, cost I think about £7 for two, goes right to the edge of the screen, and I have a clear silicon case on it that cost about £8-9. It butts right up to the screen protector which gives a bit more protection, and there’s a place to connect a lanyard as well – I’ve got an old Garmin lanyard with a quick-release buckle attachment on the end, and I’ve used 50lb fishing leader to attach the phone to the lanyard, which I wrap around my belt, so if it slips out of my pocket, it can’t go very far. Works perfectly, and with virtually no extra bulk.