There is currently not really such a thing as a Nutils adapter. Coupling Nutils is so simple that directly calling the preCICE Python API from the application scripts is the way to go.
Updated 11 Jan 24

The best way to learn how to couple a Nutils application script is to look at some examples:

To install a specific version of Nutils use, for example: pip3 install --user nutils==6.3.

Version 8 requires bottombar as a dependency. pip might automatically install version 2.0, which has known issues when used with preCICE. A patch was implemented in version 2.1, thus a workaround is to explicitly re-install version 2.1: pip3 install --user bottombar==2.1.