Thanks MJ, I appreciate your questions and have responded below.
You want it to be compact, but how compact? => I'm flexible on this. Ideally I would get something I could stuff in my pocket, but I know that may not be realistic. I would say anything smaller than a full-on SLR sized camera would work. In other words, I hope to be able to put the camera into a pocket in my backpack versus having to carry its own dedicated bag.
What are you prepared to do when it comes to processing your images? => hopefully nothing. I don't do any processing to my smartphone pics so, hoping for something equivalent but in a better camera.
I don't understand the 3x optical zoom thing. => my smartphone has 2x, 3x, and 10x optical zoom. I don't expect to get a nicer camera with that high of an optical zoom but I also don't want camera that has NO zoom, so I figured 3x was a good compromise.
Do you want a camera with interchangeable lenses, or do you want one with a fixed lens that would save you some lens decision headaches? => ideally the latter, but I'm open to the former.
Also, you didn't specify a budget. => say $750
Sound to me that considering your requirements (stabilization, small, great colorful snaps in auto mode), a high end smartphone is what I would recommend, and the S23 Ultra is already a killer phone for that. => haha you may be right! But in my naivety I'm hoping to find something that takes nicer shots with minimum fuss.
Okay, so after some thinking, it sounds to me like a nice premium compact camera would fit the bill just fine. However, be aware that cameras don't play the resolution game like phones do : a lower resolution (12-16MP) might very well deliver sharper results than a 50MP smartphone camera. So don't take the resolutions at face value comparing them with smartphone sensors.
So to look at your criterias, you want :
a small-ish camera that has preferably a fixed lens, a 3x zoom (I've done some research in the meantime, and the "1x" lens on most phones is about 24mm equivalent, so a 3x zoom would be equivalent to a 72mm or something similar), under $750.
There aren't a ton of cameras that fit those criterias
AND have better image quality than a samsung S23 Ultra, but there are a few.
The first two obvious ones to me are the premium range of Lumix compact cameras, like the LX100 mark II and the LX10/LX15.
The LX100II has a larger 17MP sensor (which is a cropped micro four thirds chip) compared to the LX15 that has a 1" sensor. That being said, the LX15 has a wider lens, so the difference in image quality is well compensated there. Both lenses have a lens with arounx 3x zoom capabiltiies (the LX100 has a 24-75mm equivalent, with f/1.7-2.8 apertures, so overall pretty good ; the LX15 has a 24-72mm equivalent lens with an f/1.4-2.8).
The LX15 is ligher, smaller and cheaper than the LX100II, but the LX100II has better controls, a hotshoe to connect extrernal flashes, and a vewfinder. On the other hand, the LX15 has a tilt screen and a pop-up flash, but no ability to connect an external one. Neither camera has IBIS, however both feature optical image stabilization in the lens.
The last one I'd recommend is something like a Sony RX100 mark IV or mark V. Both of those models have a 24-70mm equivalent lens (so about 2.9x zoom ratio) with an aperture of f/1.8-2.8 (very similar to the other two). Autofocus and burst rates will be better than both the Lumix cameras, and unlike the Lumixes, that have either an EVF or a pop up flash, the RX100IV and V have both. The difference between them is mostly about AF performance and video (and price).
Considering your requirements, this seems like the three best options available on the market short of getting into ILC territory.
In terms of image processing, I feel like the Lumix options give you more for your money when it comes to image profiles, color correction etc compared to the Sony, but definitely go look at reviews for both of them.
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(G.A.S. and collectionnite will get my skin one day)