There is so much that it depends on...
The D850 (and D810/most cameras) never delivers more than 8bit/channel color (24bit RGB). So there is no penalty to using 8bit there...
But it does nearly approach 14EV of dynamic range capability at low ISO's. So, if the scene you're trying to record has/requires the dynamic range, then you are better using 12bit NEF's below ISO 12,800, and 14bit NEF's below ISO 400... if recording raw files.
It requires 1bit of data/EV for a raw file (exposure and bits are both logarithmic). But if the scene has a low dynamic range requirement, then 8bit might not really matter there either.
And it does not require 1bit/EV for a processed jpeg/tiff. An 8bit image with a gamma curve applied can display approx 12EV of dynamic range (by compressing excessive/useless highlight data). So again, above ISO 400 there isn't much penalty to 8bit.
The real difference comes in the file processing... both a jpeg and a tiff are processed by the camera based upon the picture styles/settings chosen... and any additional information not required for the output image is discarded. The only difference between the camera generated tiff and jpeg is that the tiff data is not compressed (much larger files) and jpegs are lossy compressed (even more data discarded).
And no, you cannot get 16bit data by storing 8bit data in a 16bit file format. However,
you can get much greater accuracy during editing by converting an 8bit image to 16bit... I highly recommend all edits be made in 16bit when possible (minimizes banding and other processing errors).
To simplify... w/ the D810/850 (and most cameras really)... above ISO 400 there is no real penalty to recording 8bit jpegs/tiffs *
IF* the camera processing produces an image that is as desired SOOC; or nearly so and additional processing is done in 16bit (in LR, or as 16bit tiff/psd in PS or other program).
Otherwise you are better off recording raw files; 12bit is fine above ISO 400, and there is
some small benefit to using 14bit below ISO 400. And in your case you would then want to use software like Nikon's free NX Studio to export/convert the 16bit raw file format into a 16bit tiff format for your final program (the actual bit accuracy w/in those files will depend on what the camera generated).
Personally, for what you are doing I would probably start by choosing a very mild picture style (neutral or flat) for the in-camera processing and record jpegs for stacking. It will just be so much less demanding and save a ton of space/time... you can always decide to try raw>tiff later if you find some shortcoming to using jpegs.