`noncomputable` error on definitions without data

Prerequisites

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• Reduce the issue to a minimal, self-contained, reproducible test case.
  Avoid dependencies to Mathlib or Batteries.
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Description

The error lean.dependsOnNoncomputable is thrown on definitions of a type whose elements contain no data at runtime. For example, def setoid : Setoid Nat := Classical.choice ⟨Setoid.trivial Nat⟩ fails, even though elements of Setoid Nat consist of a pair r : Nat → Nat → Prop which is a predicate and so is erased a runtime and a iseqv : Equivalence r which is a proof and so is also erased at runtime.

Context

I encountered this error after upgrading my Setoid theorems from an earlier version of Lean. See Zulip.

Steps to Reproduce

def prop : Prop := Classical.choice ⟨True⟩
def subtype : { p : Prop // p } := Classical.choice ⟨⟨True, trivial⟩⟩
def setoid : Setoid Nat := Classical.choice ⟨Setoid.trivial Nat⟩
def unit : Unit := Classical.choice ⟨()⟩

Expected behavior: prop, subtype, setoid, and unit will behave similarly, since their types do not contain any data at runtime

Actual behavior: only prop is fine, but the other three throw "error: Classical.choice not supported by code generator; consider marking definition as noncomputable"

Versions

I tested versions v4.31.0, v4.30.0, v.4.29.0, ..., v4.17.0

• prop works on all the versions I tested
• subtype fails on v4.21.0 and below but works on v4.22.0 up to v4.28.0 and fails on v4.29.0 and above
• setoid fails on all the versions I tested
• unit fails on all the versions I tested

Target: x86_64-w64-windows-gnu Windows

Impact

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Start with the four minimal definitions in the issue and reproduce the Classical.choice code-generation errors on the current Lean version, comparing prop, subtype, setoid, and unit. Trace the compiler's treatment of erased predicates, proofs, and data-free types; done means these definitions receive consistent behavior without incorrectly requiring noncomputable.