Challenger 300
Flight Crew Air Transport Pilot (ATP)
Situational Awareness; Workload
Conflict Airborne Conflict
Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action
Human Factors
While approaching Branson; Missouri and expecting the visual approach for runway 32 from the ATIS report we were unable to get visual on the airport until almost directly above the airport. We were in contact with Springfield approach and informed the controller that the visual was not going to work and we needed vectors for the ILS32 due to deteriorating weather conditions.The controller issued a vector to the southwest of the airport and we were told to descend to 3200 feet and expect the ILS32 which we complied with. The time periods between assigned heading/vectors seemed very excessive and the pilot flying and I commented that he seemed to be operating another frequency or distracted. After receiving a heading back towards the localizer; I noticed another aircraft on TCAS at our same altitude that seemed to be on a converging course about 4 miles away and closing. We were in and out of the tops and mostly IMC conditions but I was able to get a visual on the aircraft occasionally.When we were about 7 miles from the DILME intersection on a northeast heading I (Pilot Monitoring) queried the controller about the approaching aircraft and received an immediate right turn to the southwest and a climb from 3200 to 4000. At this time we received a TA from the TCAS and turned right and began the climb. The TCAS was set on the close in range (5 NM) and showed us less than half a mile from the other aircraft (Cessna Caravan) and at the same altitude. While we were climbing and turning the Pilot Flying got a visual on the aircraft and later stated that we were so close that the other aircraft's pilot was clearly visible.After clearing the traffic conflict and receiving vectors back towards the airport for a second time I asked the Springfield Approach controller how the near miss we experienced happened and he stated 'That was my bad; sorry'. The rest of the flight continued normally and we executed the ILS32 and landed without any more issues.
CL-350 First Officer reported an airborne conflict on approach to BBG that he felt was related to ATC Controller workload.