I'm still rather fond of my D3s, and find it to be quite a capable camera in 2023.
I'm a somewhat recent(within the last month) owner of a D5, and the D5 absolute smokes it in every metric but it's also an order of magnitude more expensive.
12mp isn't as terrible as some would have you think, although it definitely shows its age compared to high resolution bodies(I have the full D8xx series, and now primarily use a D850). Still, though, getting the most out of the high-res bodies basically requires cutting edge glass and excellent technique, and in practice I find that I'm often pushed to get appreciably more detail when handheld out of my D850 than my D5. A tripod, good technique, and modern high end glass changes things(my 24-70 f/2.8E is the best to show the difference and also my newest lens, but I can see it on my older 70-200 f/2.8 VR1 and 300 f/2.8 VR1). Noise and DR are still respectable. The D3s is a big improvement in noise(or at least based on the D700 I had-I've never owned a regular D3) but I realize you're asking about the original D3. Increasingly newer single digit bodies do give big improvements in noise, but again they also jump up in price quite a bit(The Df is excellent also, but these days the D4 is a lot less expensive with the same sensor). You do get more DR out of the D8xx bodies, but again the D3 is still respectable.
AF is still quite respectable. It does have 3D tracking, but will need a bit more help to pick the initial focus point than newer systems(especially the D5/D850/D500 system). It's also easy to "trick" into jumping if something goes in front of your tracked subject(newer cameras have a delay for this). Judicious use of AF lock can help this, although if using back button focus I find lenses with focus lock buttons to be very helpful. It doesn't have anywhere near as many focus points as newer cameras. I'd say overall AF performance is comparable to my D800. The ONE place where it does beat the D800 is when using screwdriver lenses, but that's a general rule for the single digit bodies as they tend to have bigger motors.
I've generally had good luck with original EN-EL4 batteries continuing to work well, although I have a few aftermarkets that are fine also.
There's no getting around the D3 being big. Although I started my(serious) digital journey with a D2X, and still have the D3s and now D5, there's a reason why the D850 and other D8xx cameras have become my main ones. Higher resolution aside, they just weigh a lot less and are smaller.