So a baseline Barbarian in D&D 5e gets Fast Movement at 5th level (Player's Handbook, p. 49):
your speed increases by 10 feet while you aren't wearing heavy armor.
The Storm Herald Barbarian subclass gets a feature at 6th level that can grant you a new, non-walking, movement speed if you pick the Sea environment ability (Xanathar's Guide to Everything, p. 10, emphasis mine):
Sea You gain resistance to lightning damage, and you can breathe underwater. You also gain a swimming speed of 30 feet.
Does the Fast Movement feature interact with this swim speed for an overall swimming speed of 40 feet?
Does Fast Movement in general interact with non-walking speeds? If so, would it apply to a swim or climb speed granted through a different method, like a spell or magic item?