Help me choosing a compact camera

Hello everyone!
This is my first post in this sub-reddit! I'd like to ask your expert opinion about my next purchase, but first some context:

I ditched my smartphone and am now looking for something that would replace it as an everyday carry (my smartphone was an iPhone 12 Pro Max). I am a dad, so I mostly take pictures and videos of my family, vacation pictures and I like to dabble in some street photography just for fun.

I started looking for a compact camera that would give me good quality pictures and videos (and I'd like it to be a clear step up over the iPhone if possible).

Here is my compiled questionnaire:

Budget: up to 800

Country: USA

Condition: used is fine

Type of Camera: can be point and shoot and mirrorless, would love to have something more versatile but it's not an absolute must.

Intended use: hybrid shooting (family pictures and videos, some outdoor videos and picture as well)

End use: Personal photo album

What features would be nice to have: A good autofocus (I hate the autofocus on my lumix g85, it costantly hunts for target during videos)

Portability: How portable does it need to be?Pocketable

Cameras you're considering: After much research, I ended up with the following options (I know they are wildly different, but hear me out :D )

Asp-c / micro 4/3 options that are somewhat smaller:

-sony a5100

-sony ezv-10 (I included this because of 4k vide. Even tho is primarily geared towards video, its massive sensor takes some great pictures too)

-Lumix gf9

-if you have any other suggestion for cameras with a micro 4/3 or asp-c sensor that are pocketable please let me know. They don't necessarily have to hav swappable lenses!

mid size pocketable ones:

sony zv-1 (in the list because of 4k. I heard it takes great pictures too)

rx100 V

canon g9x mark II

super pocket ones:

samsung nx mini

canon s120

fujifilm xq1

Cameras you already have: Lumix G85 (clearly too big for this purpose, but I really like it. The only thing I truly dislike about it is the terrible autofocus)

Notes: One of the main things of course is pocketability. I would love if it can fit in jeans pocket. However I would also really like to have a larger sensor if possible. (no, unfortunately no ricoh grIII for me because of the terrible video capabilities)

Do you have any recommendation? Which one between these would you choose and why?

My main concern with the ones in the super pocket category is that they would actually end up being a step down from iPhone 12 Pro Max. They certainly would in video capabilities.

Let me know your thoughts!

Thanks