linarith can no longer solve a simple problem

Adapted from zulip:

This works in mathlib3:

import data.real.basic

example (a b c d e : ℚ)
    (ha : 2 * a + b + c + d + e = 4)
    (hb : a + 2 * b + c + d + e = 5)
    (hc : a + b + 2 * c + d + e = 6)
    (hd : a + b + c + 2 * d + e = 7)
    (he : a + b + c + d + 2 * e = 8) :
    e = 3 := by
  linarith

but no longer works in mathlib4:

import Mathlib

example (a b c d e : ℚ)
    (ha : 2 * a + b + c + d + e = 4)
    (hb : a + 2 * b + c + d + e = 5)
    (hc : a + b + 2 * c + d + e = 6)
    (hd : a + b + c + 2 * d + e = 7)
    (he : a + b + c + d + 2 * e = 8) :
    e = 3 := by
  linarith (config := { oracle := .fourierMotzkin })

Possibly related to #2717

Start by reproducing the provided Lean examples and inspect the linarith tactic's Fourier–Motzkin oracle. Compare the behavior with the related #2717 issue; the work is done when the shown rational-number example is solved again with the stated configuration.