Q. What TIFF formats/pixel depths does NEXTSTEP support?

A.
(I say color rather than 8bit or 24 bit cause 2.0 
Icon says it's 24 bit and tiffutil -icon says 8bit.  Your guess.)

yes it's really 8 bits 
2^8=256 or the number of intensity levels (one lowly byte)
times the number of samples (or planes) per pixel --- 256 ^ 3= the 16.77 mill colors possible.
one sample is the green channel, one the red, one the blue.

(24 bits is a 'understood' misnomer its 8bits+8bits+8bits)
then there is the 8 bits of alpha channel which is non standard.
which makes our full 32bit NeXT Dimension Board

12bits is three levels (RGB) of four bits each sample
2^4=16 levels of intensity
three of them makes 16 * 16 * 16 = 4096 colors or the NeXT Turbo colors.

Now for the part I don't know as much about:
besides the stuff in NXTIFFPboardType in the developers online manuals
look under 
findImageNamed:
bestRepresentation
in the NXImage object. (look at the rest for lots more)
there you will see that the icon for a application can also be a EPS file and a description of how the "best representation" is found. 
Best representation being a comparison of the current environment and the tiffs in the file.
In theory you could have a hi-res 400 dpi image packed in to you tiff and it <should> be used for print out on the printer. I haven't checked it out.

One thing that does not work, however, is 
viewing both the color and 2bit images on 
two-headed cubes - at least this doesn't work in 2.0 
I don't know bout 3.0.  I had hoped to be able to view 
the color version of the tiff in the color monitor, 
and the 2-bit version in the megapixel monitor,
however that doesn't work.

It would seem the problem is more along the lines that the workspace is not updating the environment variables for each screen rather it is defaulting to the deepest of the two.
(this is conjecture from a mono-person). This has to do with the off screen cache too.