You can load the downloaded solution using the property DTE.Solutionand the active document via DTE.ActiveDocument. Actually, there is no "active project" because you never activate projects, you only open solutions (which may contain several projects) and files (which are in projects).
I suspect time tracking requires a current solution, probably enough. However, if you need to specifically distinguish between projects in a solution, you can do this using DTE.ActiveDocument.ProjectItem.ContainingProject.
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