`rw [foo] at *` rewrites `foo` itself

Description

In Lean 4, if you use rw [foo] at * then it rewrites everything including foo.
If you had foo : x = y then you obtain foo : y = y afterwards.
It might happen that foo would be useful again later.
After rw [foo] at * it is useless and foo only clutters the infoview.

Steps to Reproduce

example (α : Type) (a b c d : α) (hab : a = b) (hac : a = c) :
  a = d  :=
by
  rw [hab] at *
  sorry

Expected behavior:

I think that rw [hab] at * should rewrite a only in hac and the goal.
This is how it worked in Lean 3.

Actual behavior:

α : Type
a b c d : α
hab : b = b
hac : b = c
⊢ b = d

After rw [hab] at * you can see that hab : b = b is in the infoview.

Reproduces how often:

100 %

Additional Information

Lean 3 code

example (α : Type) (a b c d : α) (hab : a = b) (hac : a = c) :
  a = d  :=
begin
  rw [hab] at *,
  sorry
end

gives:

α : Type,
a b c d : α,
hab : a = b,
hac : b = c
⊢ b = d

Start with the Lean 4 reproduction in the issue and compare its infoview after rw [hab] at * with the documented Lean 3 behavior. Trace the implementation of rw handling for at *; done means the rewrite leaves hab unchanged while updating hac and the goal.