I only have a basic understanding of the principles of stone sculpting
and any insights are appreciated.
Use your imagination. What do you want it to look like?
D&D 5e is not reality simulation, nor does it attempt to be. Difficult terrain is ground that is hard to walk on, an area where you are slowed down by trying to move through it. This could be a pile of boulders, a swamp, mud, or just very uneven ground where no two steps are on the same level.
Assuming the caster is skilled enough to smooth the stone within the hour, such that it is no longer difficult terrain, what happens when the spell ends?
The magical effect ends. Whatever was there becomes what it was before the cantrip was cast. The duration of the magical effect is one hour.
How exactly was the stone warped in the first place?
By magic.
How does normal terrain become less difficult terrain?
By magic.
Would the effect be ascetically pleasing or would it look sloppy?
That depends upon the interaction between the player and the DM.
Use your imagination. What do you want it to look like? This is where a DM's ruling is appropriate. Tell the DM what you want it to look like. The flow of events in D&D (p. 3, Basic Rules) is:
How to Play
1. The DM describes the environment.
2. The players describe what they want to do.
3. The DM narrates the results of the adventurers’ actions.
You describe what you want it to look like. The DM rules on that with your input considered.
The philosophy that the game started with still applies. D&D 5e has tried to unify the D&D fan base, in some cases reaching back to first principles ... When Imagination Was The Only Rule ... the theme behind Rob Kuntz'1 projects.
Action required: use your imagination and describe what efforts you are putting into this bit of magic-assisted sculpture, and what you are trying to make it look like. Give the DM something to work with so that he doesn't have to do a lot of work to arrive at a ruling. (As a DM of some experience, I promise you, such efforts are appreciated).
1 Who is Rob Kuntz and what does he have to do with D&D 5e? The front page of the rule book says that the game is:
Based on the original D&D game created by E. Gary Gygax and Dave Arneson, with Brian Blume, Rob Kuntz, James Ward, and Don Kaye
The area is the ground within a 10 foot radius of you.
The wording of the spell is a little ambiguous, but it intends a 10 foot radius from the caster.
1) A previous version of the spell has a range of "Self (10-foot radius)" and explicitly states that "you cause a tremor in the ground in a 10-foot radius." (See: this older edition of the Elemental Evil Player's Companion from 2015). This indicates the original design intent.
2) The current version of the spell specifies that "you cause a tremor in the ground within range." Literally, the ground within the range of the spell includes precisely the ground within 10 feet of you. Therefore the range of the spell itself sweeps out the area: a circle with a 10 foot radius centered on you.
Yes, the new wording is dissimilar from how most spells indicate a similar area (using a range of "Self" and mentioning the nature of the area in the spell text), but I conjecture that the designers revised the spell to simplify the wording and inadvertently introduced an ambiguity.
Best Answer
RAW - the spell only damages creatures and creates difficult terrain
In 5e, spells do only what they say they do. In this case, as you say, the spell does damage only to creatures and then makes the area difficult terrain. If the spell was intended to deal damage to objects and terrain it would say so explicitly. In this case "erupting" is just descriptive of the way the dirt and rocks act, but not of any mechanical effects to the surrounding area.
The surface is covered in dirt and rocks, but the spell doesn't say from where
However, the spell never actually says if the churned earth and stone is from the surrounding area at all. As this is a magic spell, it can easily be that these are magically created dirt and rocks. After all, not all "ground" necessarily involves places with dirt and rocks together. The fact that the spell works the same regardless of where you cast it (as long as it is "ground") says that this is probably magically created debris.
Since this is an unclear area of the rules, it is up to the DM to decide how to handle them.
As DM you can tweak the effects to allow creative uses
As a DM you have the latitude to interpret spells to work in different ways than strictly RAW. For example, if this is an area in which ore was prevalent I would probably allow some of that ore to surface as part of the "fountain of churned earth and stone". This is a fun and thematic use of a spell in my opinion, and if you don't have to follow strict RAW then it seems fine to allow it.
Regarding damaging objects with the spell, it makes a bit less sense to me and I am not sure I would allow it. The damage in this case comes from the falling debris not from the "eruption". And I would be careful with ruling to expand the things a spell can affect without careful consideration of other ways it might be used once ruled. There are other spells (eg shatter) that are specifically designed to shatter inorganic objects so I feel like changing this spell to allow that would basically be giving two spells in one. That being said, if you are fine with these objections you can still allow it and see what happens.