Let me see...
Fate is not designed for zero-to-hero narratives - Mostly true. Fate is actually very well designed to express how a person changes when exposed to events in their world. The design isn't about increase in overall power, but is about change in response to events.
It's not designed for exploration and dungeon crawls - In the square-crawling sense, true. In the sense of exploring exciting, unknown, dynamic locations, totally false. You can whip out more interesting traps, terrain, and situations in FATE than in just about any other system.
It's not a game about rewarding good tactical play - Completely false. FATE is very much about engaging with the details fo a scene provided. It just isn't grid-based-movement tactics.
...players engaging an in-universe resource management minigame - True.
....or solving puzzles - false. FATE provides at least as much support for puzzles as any version of D&D does. Note how puzzles in D&D are generally things outside the ruleset?
....And sort of the action declarations that a player can make or encouraged to make will differ between games. - I admit this one seems a little hard to parse. I don't think either game really limits the declarations a player can make, but the effective ones in D&D combat heavily lean on a specific list defined by character build and abilities, and out of combat lean heavily to a restricted list of skills - D&D leans to each character having a picklist of specific actions they will generally take. I think FATE gives players more ways to boost their own chances, and so allow a soemwhat broader approach to situations than the D&D picklist. What kind of declarations the player is "encouraged to make" is determined by scenario/adventure design, and is not directly a function of the ruleset in either game.