revert fails with variable

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

revert fails with metavariables when a variable statement is used, but succeeds if a proper argument is used or nonrec is added.

Context

https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/revert.20and.20variable
affects also extract_goal in mathlib

Steps to Reproduce

variable {P : Prop}
theorem bug --adding nonrec fixes the issue
  --{P : Prop} --uncommenting this line fixes the issue
  (S : P → Prop) :
  ∃ (hx : P), S hx := by
  apply Exists.intro
  · revert P -- tactic 'clear' failed, target depends on 'bug'
    sorry

Expected behavior:

revert succeeds, and behaves identically for variables and parameters

Actual behavior:

revert succeeds only without variable

Versions

Lean 4.10.0 (also earlier)

Impact

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Start by running the minimal reproducer with Lean 4.10.0 and compare the behavior of revert P with a proper parameter or nonrec. Trace the revert tactic and the related clear failure; done means variables and parameters behave identically and the example succeeds without the workaround.