Nyquist cannot (directly) read label tracks.
In the next version of Audacity (2.3.0), Nyquist has, with some constraints, access to the same Audacity scripting commands that are available to Python. This includes being able to access label track data. The major advantage of Nyquist over Python is that Nyquist is built into Audacity as standard, whereas Python is a totally separate thing, and Python requires Audacity to be build with mod-script-pipe enabled (which currently it isn’t).
Unfortunately, because this is a totally new feature, there is not yet much documentation / support material for using Audacity’s scripting with Nyquist.
If you are interested in taking a look, there is now a “release candidate” for Audacity 2.3.0 (see: https://forum.audacityteam.org/t/release-candidate-for-audacity-2-3-0-now-available/50372/1). The manual for the development version of Audacity is here: https://alphamanual.audacityteam.org
This is probably the most relevant documentation: https://alphamanual.audacityteam.org/man/Nyquist_Macros
There’s lots of documentation for Nyquist. See: Manuals and reference material