You only get very limited information, mono or stereo and sample rate (both in the Track Control Panel to left of the waveform). The bit-depth shown there is the resolution the file is imported at according to your Quality Preferences, and not the actual bit depth of the file.
Any more information than that (such as MP3 bit rate) is a feature request for full audio properties information. I’ll add your vote for that unless you say otherwise, so we can gauge how many people would like this.
You can also try a program called MediaInfo that is nothing to do with Audacity. Avoid the installer as it is bundleware.
Set the sample rate for the export in “Project Rate” bottom left of the Audacity window.
Then File > Export, choose “Other uncompressed files”, click “Options” and choose “Unsigned 8 bit PCM”. U-Law and A-Law in that dialogue are also 8-bit formats, but using companding algorithms.
For WAV files, the bit rate = (bit depth) x (sample rate) x (number of channels). So for a recording with a 44100 Hz sample rate, 2 channels (stereo) and 16-bit depth: 44100 x 2 x 16 = 1411200 bits per second, or, 1411.2 kbps.
So in your example halving the bit depth from 16-bit to 8-bit halves the bit rate.
“File menu > Export”
Select “Other uncompressed files” as the file type.
Click on the “Options” button and select “RAW” as the header and whichever “Encoding” it is that you require.