When I had bad acne my favorite facial soaps were ones with very little actual cleansing. And from browsing Etsy and these forums I see a lot of common ingredients among acne and healing skin soaps--
Antiseptic essential oils: Tea Tree, Clove, Thyme, Lavender
Anti-inflammatory essential oils: Chamomile, Ginger, Helichrysum, Patchouli
Base oils: neem oil (antiseptic/antifungal), grapeseed oil (mild astringent), jojoba (a liquid wax but can be used at small %, close to skin's natural oils)