2S shows <10 with 6 spades. Since you have neither, it looks like a poor choice.
2N is the proper rebid. That shows 11-12 HCP, invitational. Especially with Q10x of clubs that you want lead into rather than through.
Opener should have a full opener after the 2D rebid. 1N rebid by opener is also possible.
After 1H - 1S - 2D - ?
Pass, 2H, 2S = weak signoff
2N, 3D, 3H, 3S = invitational
2S and 3S show 6s