grind: missing support for `ZMod` and non-numeral `Nat.cast`

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
  (You can also use the settings there to switch to “Lean nightly”)

Description

This succeeds:

import Mathlib.Data.ZMod.Defs

example
  (a b c : Nat) (h : c = a + b) :
  (c : ZMod 3329) = (a : ZMod 3329) + (b : ZMod 3329)
  := by
  simp only [h]; grind

But this fails:

import Mathlib.Data.ZMod.Defs

example
  (a b c : Nat) (h : c = a + b) :
  (c : ZMod 3329) = (a : ZMod 3329) + (b : ZMod 3329)
  := by
  grind

Versions

4.27.0-rc1

Impact

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

Start with the two minimal examples in the issue and the grind tactic entry point, reproducing the difference between the versions with and without simp only [h]. Done means the second example succeeds while supporting ZMod and non-numeral Nat.cast without Mathlib or Batteries dependencies.