An AC separation can nag you for quite a while and can be uncomfortable for quite a bit even after healing completely. I would say to make sure to get a proper warm-up/mobility/activation routine going before lifting, including good thoracic mobility, activation scapular stabilizers, etc.
I would avoid heavy full range bench and dips for a bit longer. Push ups, loaded or unloaded, should be fine as the scapula are free to move and not forcefully pinned down by the bench. Front squats may be uncomfortable for a while as well due to the bar placement.
I'd say for a mild AC sprain, you should be fine to get back into lifting after 4 weeks. Just be smart about things - if it hurts excessively, stop doing it. It would benefit you to add in some "prehab"/rehab based exercises into your lifting as well - focus on serratus, rhomboids, lower/mid traps, and rot cuff, along with keeping proper mobility of the t-spine.