I have no need for gnomes in the least. However, this little bit has drawn my attention favorably. Well done! My biggest issue is that they are too similar to either halflings or dwarves, and I prefer the different races to be strongly themed. I am following the thread with interest, and look forward to someone changing my mind!
Fair! While I prefer gaming worlds to be built with stuff strongly differentiated races very low on the priority list, I do think that gnomes are mostly just not well presented in 5e, but the 3.5 and 4e gnomes nothing like halflings and very little like anyone else.
3.5 gnomes are basically 5e’s
rock gnomes. They are friendly, curious, and are beings of laughter and familial loyalty and creation. They have a potential strong place in a world as those responsible for the invention of crossbows, or water wheels, or water screws, windmills, etc.
If you want a race of people who see a strange and terrible monster they’ve never seen before, and immediately get out a notebook, rock gnomes are your best bet.
What they should have in 5e is tinkers tools and one other artisans tools, and something related to
invention, because they’re just as likely to be painters or sculptors, as cobblers or artificers or inventors.
Forest Gnomes are basically the 4e gnome, which was a Fey creature with gemlike eyes and wild hair, who could turn invisible. They love illusions, and live in the deep forests near places close to the Feywild, and make their homes in burrows under the roots of trees, and bigger folk often walk through without ever knowing they were in a town.
Gnomes have off and on spoken to small and/or burrowing animals, been illusionists, and been associated with alchemy (true to their IRL origin as earth spirits in the writings of the alchemist Paracelsus) and inventions, trickery, and a jovial jokester nature.
I will admit that rock gnomes often are depicted basically living in hobbit homes, but hey they’re little earth spirit guys, where else they gonna live?