I hate phone cameras with a passion, I'm also quite anti cameras without viewfinders. From experience, not some weird irrational hatred. They just don't work for me, I shoot for pure enjoyment, that for of camera is just an exercise in frustration for me.
I'm also not keen on carrying things around in my pockets. That includes wallets, and phones. So a camera that fits into a pocket simply doesn't register on my radar.
I've nearly always got some type of bag/backpack on me, for dragging around wallet/phone etc. I take my lunch to work with me each day (my Wife looks after me very well there) so I've got a bag with me for that. So in goes a camera.
When we go shopping, hiking, mountain biking etc I've always got some sort of bag with me again. For a bottle of water, a warmer shirt or jacket, spare tube and a couple of hand tools for the bike, so in goes a camera again.
When we go on holidays, I always carry some sort of backpack for essentials. Passport, wallet, phone, umbrella or shower jacket etc, so in goes a camera again.
I used to like shoulder type bags, but injuries like a broken hip, and back trouble related to that caused by accidents, have stopped me using them. The weight on one shoulder just sets off back muscle pain. Took me quite a while to figure out what was causing it, as soon as I dumped the shoulder bags I was away. So backpacks have become the norm now.
So after waffling on about all that, I simply take my Panasonic S5 full frame camera with me. Nearly everywhere. With some sort of Ultrawide lens, as well as some type of standard-ish zoom or Prime.
At the moment overseas on holiday, it's my Sigma 28-70mm F2.8, it's light (470 GM's from memory), sharp, possesses an very handy zoom range, not expensive, and a pleasure to use. Plus my Lumix 18mm F1.8 It's a great setup. For just strolling around.
I generally just hold the camera in my hand as I'm wandering about as it has a nice ergonomic and comfortable grip, and don't even notice it.
Sunday we went for a hike up a mountain close by, about 800 metres of vertical elevation over about 2kms. It was freaking steep, but I just carried my camera the whole way. No straps or holders, I can just hook two fingers under the camera grip and it hangs there with little to no effort.
A couple of snaps from along the way
My model for the day
Sorry it got a bit long winded, but I find it an absolute pleasure to have a great camera with me that I thoroughly enjoy using, rather than something I'm fighting with, just so I can fit it in a pocket.
Edit -yeah, we did make it to the top see
Although we cheated and did the touristy thing, and caught the cable car the last 1/3 of the walk back down