How does curiosity manifest itself in forest gnomes?
I love playing them, but I've never found them innately curious – to me they are more caretakers and homebodies, with homes made of leaves and petals
Arguably, the issue with gnomes is that (like the Ranger class) they were poorly defined at the beginning of D&D, and have suffered ever since from the lack of definition.
In the beginning, gnomes were simple ... small dwarves. Really. If you look to the 1e PHB and Monster Manual, they are described exclusively in relation to "their larger cousins, dwarves ..." In many ways, gnomes were simply dwarves who lived in rocky hills instead of mountains.
There just wasn't a lot to go on. Of course, lore began to spread around them, often because of certain peculiarities; for example, gnomes were often thought of as curious and "tricky" not because of the racial description, but because they were the only race, other than human, that could become an illusionist (and could multiclass into illusionist). But, again, there just wasn't a lot "there" for a lot of the early history of D&D.
That meant that when the later "flavors" of gnome were introduced, specifically the tinker gnome (in Dragonlance) and the playable Deep Gnomes (UA), those flavors kind of overwhelmed the concept of the original idea- sort of like how, with the Ranger, later introductions (such as dual-wielding) often overwhelmed the original class concept.
That's why the "essence of gnome" is difficult to tease out now. You don't have some sort of pre-D&D lore that is agreed-upon (Tolkien) like you do with Elves and Dwarves and Hobb... Halflings. It's a diffuse concept, with later additions overwhelming the base.