Here’s a few bits of opinion from someone playing a Wizard who is also a Wisdom Pilgrim:
Being dedicated to Wisdom lends itself to quite a few character archetypes, but often these are not the ones you would think. Wisdom dedicants are not sages sitting on the mountain waiting for others to come to them, ready to dole out mysterious and vague plot hints - they are investigators, teachers, problem solvers, journalists and strategists. If you like playing characters that work with information and knowledge, then being a Wisdom dedicant is a good way to reinforce that. The key part of that is “work” - staying relevant in the information game is very rewarding, but it takes effort and persistence.
Look at the Auras and Hallowings to get a better grip on what Wisdom means in the Empire setting. One my favourites is the Hallowing of the Volhov - carte blanche to be a nosey parker and get involved in other people’s business. Chastisement is another great one, as is the Focus anointing. If you find yourself at an impasse, direction-wise, find a priest and get them to apply Religion to your character.
Wisdom dedication can be applied in pretty much every part of the game. If you choose to get dedicated to Wisdom and make that an important part of your character, you are jumping into a pit full of plot, PC & NPC enemies/allies, opposing and supportive agendas, no matter what area of the game you get involved with. The crossover potential for Wisdom characters is massive, and all information is useful somewhere - you just have to throw it at the right things (and finding the right things is a key part of the Wisdom brief).