Does the word 透露 ("leak") only refer to something undesirable?
Question: Does 透露 only refer to something undesirable?

No, the things that got 透露 (revealed) are undisclosed information, Both 'reveal' and 'information' are neutral term
The correct term for 'to leak out (dark secret)' is '洩露 (黑暗的秘密)', Using 透露 would be too neutral
Similarly, we say 洩露醜聞 (leak out scandal), not 透露醜聞 (reveal scandal)
If you look at the following sentence &quot;美國總統在談話中透露/洩露出他發動戰爭的意向&quot; (The President of the United States revealed his intention to wage war in his conversation), you can see even '發動戰爭的意向' is not always negative because you can use either 透露 or 洩露
Meanwhile, 洩露 cannot be replaced by 透露 in &quot;美國總統在談話中洩露了他貪污的秘密&quot; (The President of the United States revealed/ give away the secert of his corruption in his conversation)