possibility to categorise / 'tag' shortened urls

I don't understand what you mean by "tag shorten", could you provide an example?

I guess the question here is related to categorise/add tags to each shortened URL. (i.e. fieldable entities)

The description on the project page says "Views integration. Short URLs are displayable objects." - does that mean that they already are fieldable entities?

(I have not tested this module yet, but certainly would need to categorise such shortened URLs, so this is my starting point in judging whether to test this module or not.)

IMO, this very specific and should be in a separate module.