[Scheduling] Add interface to manage solutions

`Problem`s contain two kinds of properties, i.e. input and solution properties. A common use-case is to make small modifications to an instance (cf. #7544) and re-schedule. To that end, it would be helpful to design and implement an interface across the problem hierarchy that allows to clear, import and export solutions.

Start by reading the Problem hierarchy and the related use case in issue #7544. Define what the cross-hierarchy interface must do for clearing, importing, and exporting solution properties, and consider the issue complete when those operations are consistently available across the hierarchy.

Written by the indexing model from the issue text.