VMO 2022 — Academic year 2021–2022, both days Question 4

For positive integers $n\lt m$, let $s(n,m)$ be the number of positive integers in $[n,m]$ coprime to $m$. Find all integers $m\ge2$ satisfying both:
(i) $\dfrac{s(n,m)}{m-n}\ge\dfrac{s(1,m)}m$ for every $n=1,2,\ldots,m-1$;
(ii) $m^2$ divides $2022^m+1$.