Use new infrastructure in `AnalysisCallback`

A new infrastructure to register sources and their dependencies has
been introduced in `96378d2`.

This commit brings the required modifications to `AnalysisCallback`,
so that it uses it.
Use new infrastructure in `AnalysisTest`

A new infrastructure to register sources and their dependencies has
been introduced in `96378d2`.

This commit brings the required modifications to `AnalysisTest`,
so that it uses it.