I'm losing the unique ID's of features when using Dissolver, which is problematic for the features that have multi-part geometries, because I'm unable to aggregate back the multi-part features based on this unique ID. How could I overcome this issue?

If you have the Group By set to the unique id it should be retained after dissolving

The only problem is, I have the Group By set to the state code (as I want to form dissolved groups by state) but this results in a loss of the unique ID's (FIPS code for each tract). My only idea at this point is to repeat a dissolve and aggregate process (using the unique ID's as the Group By parameter for both transformers) for each state by first filtering out Census Tracts that belong to that state, but this would be quite inefficient.

I'm not sure I quite understand your requirement, but you can put both the state code AND and unique ID as group by, in which case it is the combination of these values that is considered.

You can also configure the Dissolver to generate a list attribute containing the attributes from all the polygons that were dissolved.