Thats a good question. It doesn't look like its explicitly documented anywhere as to which packages deal.II requires Trilinos to be built with (i.e. utilises directly or offers some wrapped functionality for). I'll make a note to do this on the GitHub repository.
Hints to the answer come from the recommended build instructions for Trilinos, which can be found
here, and the documentation for the Trilinos-related functions that are compartmentalised in their own namespace as documented
here. From the latter you see that deal.II primarily offers wrappers for classes associated with linear algebra. On the
tutorials is a list of examples that use Trilinos. There is also some Sacado-related functionality (see, for example,
here and
here), but to what extent I'm not sure.
If I'm not mistaken, the build configuration for Trilinos is set by
this script which implies that deal.II links to the following libraries: