Its fixed for me
Logitech Control Centre still doesn't see the mouse however, but I don't much care about that anyway. Mac OS seems to take care of it fine regardless.
Spend four bucks if you have extra buttons you want to use on it for the BetterTouchTool works great with mine(MX Performance Mouse) better than the LCC ever did.
Without LCC installed, Smooth Scrolling is fixed on 10.12.2.
Since I prefer my specific LCC settings for scrolling (1/2 tick for speed, 1 tick for acceleration), I tried installing LCC (v3.9.5) again. After installation (and reboot), Smooth Scrolling works great, but highlighting text+scrolling (to highlight) still loses focus on the selected text.
(Reminder: to uninstall LCC, go to Finder's "Go" menu -> Utilities -> LCC Uninstaller)
After uninstalling LCC again, I confirmed that scrolling+highlighting works fine.
10.12.2 did not fix my problem. Scrolling seems smooth enough, but I still have the unbearable lag when I grab something with the mouse button and use the trackpad to move it. (That's how I work; the mouse is only for the buttons and scrollwheel -- left hand -- and the trackpad is for moving around on the screen -- right hand. It's an edge case, but it works for me and I find it the most efficient way I've ever worked. Two-handed like that is very "minority report" and it saves my wrists.)