`exact?` suggests term that does not work

Prerequisites

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• Check that your issue is not already filed:
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• Reduce the issue to a minimal, self-contained, reproducible test case.
  Avoid dependencies to Mathlib or Batteries.
• Test your test case against the latest nightly release, for example on
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Description

In this code:

inductive Odd : Nat → Prop
  | one : Odd 1
  | add_two : Odd n → Odd (n + 2)

theorem odd_iff {n : Nat} : Odd n ↔ n % 2 = 1 := by
  refine ⟨fun h => by induction h <;> omega, ?_⟩
  match n with
  | 0 => simp
  | 1 => exact fun _ => Odd.one
  | n + 2 => exact fun _ => Odd.add_two (odd_iff.mpr (by omega))

example {n : Nat} : n % 2 = 1 → Odd n := by exact?

the suggestion we get from exact? is Try this: exact fun a => (fun {n} => odd_iff.mpr) a, but this does not work. Accepting the suggestion leads to the two errors

failed to infer binder type

and

don't know how to synthesize implicit argument 'n'
  (@fun {n_1} => odd_iff.mpr) (?m.2120 a) a
context:
n : Nat
a : n % 2 = 1
⊢ ?m.2119 a

Expected behavior: exact? suggests some invocation of odd_iff that works

Actual behavior: Suggestion leads to error above

Versions

4.12.0-nightly-2024-09-19 on live.lean-lang.org

Impact

Add 👍 to issues you consider important. If others are impacted by this issue, please ask them to add 👍 to it.

Start with the self-contained Odd/odd_iff reproducer and the exact? invocation described in the issue; reproduce it on the Lean nightly release using live.lean-lang.org. Trace the suggestion generation path for this case, then verify that the suggested invocation compiles and matches the expected behavior.