An Air Carrier pilot reported during initial climb from takeoff ATC turned them to avoid an arriving aircraft executing a go-around 300 to 400 feet above them.

Narrative

We were cleared to line up and wait Runway 28 in SAV. I looked for traffic on final but did not see anything. Just before turning onto centerline; an aircraft checked in that was on Visual Approach Runway 28. Tower told them to continue; traffic is holding in position. This triggered me to look once again for any traffic on approach but once again I did not see anything. We were cleared for takeoff on Runway 28 and told to fly runway heading. I was concentrating on monitoring airspeeds; engine indications; callouts; etc. During the take off roll Tower told the corporate aircraft to 'go around left side.' At the time I did not hear or comprehend there was an aircraft just above us going around. My focus was on ensuring our aircraft is performing normal for a rotate at V1. At approximately 200 ft. AGL Tower Controller told us to turn right heading 310. I read back the clearance then Tower said 'traffic is going around just off the left side heading southwest bound.' I responded with negative contact. This was the first time we were advised of any aircraft near us. I glanced at the TCAS and it appeared the traffic was on top of us 300 to 400 ft. above us. I looked out the window and saw the traffic close proximity to us turning southwest bound. I estimate the traffic was about 500 ft. away when I made visual contact. After being handed off to the departure controller I asked if the spacing was OK on take off and he responded with NO.When told to line up and wait AND there is traffic on approach to that runway I am used to hearing something like 'Line up and wait; traffic 3 miles out.' This was not communicated to us. Non standard phraseology was used by the Tower when he instructed the corporate jet to 'go around; fly left side.' The corporate pilot was confused what exactly the Tower wanted them to do. When we were notified at 200' to turn right 310 there was no urgency. If Tower needed us on a 310 that low to the ground I would expect something like this; 'Turn right 310 immediately for traffic.'I believe airlines are pushing ATC to try and takeoff and land too many aircraft. Many times I hear 'cleared for immediate take off.' Even though we did not get that clearance this time; I think the controller wanted to get us off the ground because we had already had a short delay in receiving our take off clearance.