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A workaround is:

sage: f = function('f')(x)
sage: g = diff(f, x)
sage: f
f(x)
sage: g
diff(f(x), x)
sage: eq = g + f == x - 1
sage: eq
f(x) + diff(f(x), x) == x - 1
sage: f_1 = function("f'")(x)
sage: f_1
f'(x)
sage: eq_a = eq.substitute({g: f_1})
sage: eq_a
f(x) + f'(x) == x - 1