On the third floor stair landing there is a wall to your right, a counter hugging the outer wall of the tower, and around the curve to your left is a closed door.

On the counter there are still some odds and ends, flasks and vials remining in stands, there are a dozen that are still full though the labels are faded and illegible. There are some wooden crates underneath containing dusty glassware, some broken. It looks like this was once a laboratory of some kind.

Spoiler: Detect Magic
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With detect magic going you see that 5 of the vials/flasks have faint auras: Transmutation (2), Evocation (1), Abjuration (1), and Conjuration (1). You also feel the strong source of magic from behind you in the bartizan.