Regression in v4.33.0-rc1: `simp` creates type-incorrect goals at `.implicit` transparency

Prerequisites

• Check that your issue is not already filed:
  https://github.com/leanprover/lean4/issues
• 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
  https://live.lean-lang.org/#project=lean-nightly
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Description

When updating DyLean to v4.33.0-rc1, I noticed the following regression:
the tactic simp can transform a type-correct goal (at .implicit transparency) into a type-incorrect goal at .implicit transparency)

def f {a: Type} {p: a → Prop} [DecidablePred p] (x: a) : Option (Subtype p) :=
  if h: p x then
    some ⟨x, h⟩
  else
    none

def g {a: Type} {p: a → Prop} (x: Subtype p) : a :=
  x.val

set_option linter.tacticCheckInstances true

/--
warning: produced tactic goal is not type-correct at `.implicit` transparency; consider using propositional rewriting or marking some of the following as `@[implicit_reducible]`:
  g
Full error:
  Application type mismatch: The argument
    inst✝ (g ⟨a, b⟩)
  has type
    Decidable (p (g ⟨a, b⟩))
  but is expected to have type
    Decidable (p a)
  in the application
    @dite (Option (Subtype p)) (p a) (inst✝ (g ⟨a, b⟩))

Note: This linter can be disabled with `set_option linter.tacticCheckInstances false`
-/
#guard_msgs in
public
example (a: Type) (p: a → Prop) [DecidablePred p]
  : ∀ x: Subtype p, f (g x) = some x
:= by
  simp [f, g]
  grind

Context

Likely stemming from #13895: adding the option set_option backward.isDefEq.respectTransparency.types false fixes the issue.

Steps to Reproduce

Expected behavior: simp closes the goal, and the linter does not trigger

Actual behavior: simp does not close the goal, and the linter does trigger after a call to simp

Versions

• "4.33.0-rc1"
• "4.34.0, commit 323137b022369d56a044ae5af01d1efd55872361" (on live.lean-lang.org)

Impact

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Run the self-contained reproducer against v4.33.0-rc1 and the current nightly, focusing on simp at .implicit transparency and the linter.tacticCheckInstances warning. Investigate the interaction with backward.isDefEq.respectTransparency.types, using #13895 as context; done means simp closes the goal without producing a type-incorrect goal or triggering the linter.