I do suspect that over insanely long periods an otherwise undisturbed physical object would flow-sag at some rate under the influence of a constant force in a given direction.
No idea how long that would take, but erosion and other destructive forces appear to dominate so for practical measures any such effect is likely against the noise floor.
The "well it's technically a liquid!" because it "flows" is really not telling the whole story. Like most science, it's just more complex than can be quickly summarized with one sentence, and doesn't quite map to just high school simplifications.
so then it does flow over time, just not on a scale where it matters to us.
The physical mechanism would be similar in glass flowing in this way, so I don’t think evidence of glass flowing like this should make us think of it as a liquid instead of an amorphous solid
Glass flows a higher temperatures where it does act like a liquid, you can study glass blowing for examples, however no, room temperature glass is not a liquid and does not flow, for any practical definition of what flowing is.
What I said is true but not for glass. Pitch is a liquid even though it feels like a solid and shatters when smashed.