Cool writeup! I myself haven’t recovered from young kids yet, so I’m still rocking a nikon d800, which is great for going out shooting nature/architecture by myself (which never happens), but less so for candid family stuff. Anyway it’s nice to read your experiences.
Your D800 remains a very capable body. The three advances since them are quieter mechanical shutters (not all brands embrace them equally), pretty solid electronic shutters (so you can pass on the loud mechanical shutter when needed), and face/eye/subject recognition (makes getting the shot a lot easier). There have been some advances on the ISO noise front too, but these have been slow and steady IMO.
If you frequent dimly lit places and your kids are constantly on the move, it’s hard to beat a MLIC with a fast prime. I do occasionally miss my speedlight, diffusers, and umbrella for the effects it could create but I get by in dim light pretty well without them.
Coming from a D40, D5300, and getting back into kids with a J5 it’s kind of funny to find myself standing by a A7III, but it’s a great value these days and delivers more consistently eye/face in focus photos than a Z6II.
So sorry for the reply delay! But, that is nice to know that the more recent upgrades boil down to quieter/mechanical shutters etc. I guess I am not too worried!
But it sure would be nice to have something midway between a) the bulky D800 with very heavy sigma 12-24 or nikon 24-70, and b) my phone. :-D
M43 cameras can be a lot more compact but once you start really sweating equivalence it does get a bit messy. Modern FF mirrorless cameras, and their lenses, will also offer size/weight savings over a DSLR. Here's a very quick size comparison. Note that there is a newer version of that Sony 24-70 that reduces weight to 659 grams (vs the 1,070 of your Nikon DSLR lens). I find that my Pixel 3a is pretty good for bright light with moving subjects, but as soon as my subjects start moving and lighting drops my dedicated cameras make a world of difference.
The plus DLSRs, especially before the D40/D800 was that they were extremely repeatable. As soon as additional features, like face/eye AF got added to the mix, it all got... very hairy. "Will my camera find a face? What if it looses that face?" Aside from Canon and Sony, most modern mirrorless still struggle with front or back focusing some when using face/eye detect. Electronic View Finders can be very cool with all the information they display (level information, histograms, even flashing blown highlights/shadows in the case of Olympus, etc), but unless you're looking at a pretty modern (or $$ used) body, they tend to not be very high resolution. My A7II is serviceable, but it's not that great - especially when manually focusing. But speaking of manual focusing, one of the cool things an EVF can do is focus magnification for the thing you're focusing on as you adjust focus. Blackout free shooting with an electronic shutter on an A9 makes panning photos a lot easier for me since you can see the thing you're tracking continue to move.
/many random thoughts
All that said, used F-mount lenses are getting cheap - especially if you have a built in AF motor which you do...
Interesting points. First, yes about the F-mount lenses! I don't often use random old lenses, but, probably my most "successful" photo (big air quotes there) was when I needed a longer lens, which none of my "nice" ones are, so I slapped on an MF 135mm that someone had given me, and boom.
As for facial recognition, sports stuff, focus tracking, etc. -- I basically do most of my (non-casual/family/etc.) shooting on a tripod, at things that ain't moving (or if they are, like clouds or water, I'm using an ND filter to get that motion); so, a lot of those newer bells and whistles I don't really consider. I like lots of megapixels, low noise, a good lens, solid tripod, etc.
You already have the things you said you like, so be happy I guess. Newer sensor generations are always incrementally decreasing noise, but it's not that dramatic. Newer lenses are constantly improving sharpness, increasing AF speed, decreasing vignetting, decreasing loca, etc but they're pricey. The only thing that really stands out to me is sensor based image stabilization offered on mirrorless bodies. You can get some fairly long, and thus low noise, exposures with surprising sharpness hand held these days. M43 cameras are the clear winners here, but even on APS-C and FF sensors, the stabilization offered by sensor based stabilization is better than that offered by lens based stabilization.