A TRACON Controller in Charge reported there was a NMAC during a period of busy traffic during deteriorating weather with sectors combined and training occuring.

Narrative

I was Controller in Charge (CIC) at the time of the event and it was recommended to document my perspective; I was not the controller working the aircraft. The day was a busy day starting a few hours before the incident occurred. We had training being facilitated on two positions. I made the choice to decombine sectors X and Y because it was necessary due to the complexity. There was several factors occurring well before the incident. Photo missions; a near miss with a drone etc. I had already made the plan for the next several hours to ensure people didn't work more than 01:20 minutes or try because the complexity of the IFR traffic due to inclement weather was putting an additional workload on every position.Both training crews were on before the incident as well as a Sector Y and Sector Z Controller. The position the incident occurred on was decombined; but the other Sector A and B position was not. Not related to the event. Although I did not have a body at the moment I asked that training team if they felt comfortable combined and the trainee insisted he did. The room began to become busier I was also servicing weather and rotating around the room. I realized Sector Y position had a significant amount of planes and an 8 block was arriving for Sector Z. I actively checked and rotated around. The combined training team was getting relieved; operation as usual and a CIC was taking that combined position.Traffic increased. The trainer on X asked me to do coordination with the Tower regarding an opposite direction. I did and reported back. A little while later I heard the trainer telling the trainee to keep working through the traffic; not hesitate; and keep going. I switched to monitor the position now and using an empty scope pulled up the X sector to monitor visually as well. The Sector X line began to ring and I immediately attempted to answer the line to relieve it from their workload. Another controller helped out as well on Sector Z and got to the line before me. I then went over to that controller to ask what the coordination was. They said at ZZZ airport visibility was decreasing over our VFR entry points. I talked to the ZZZ CIC and determined VFR aircraft will need to go straight in to ZZZ. I went to both Sector X and Sector A to tell them. At that time the trainer on Sector X told the Sector A Controller to vector a ZZZ1 arrival through a different flow to buy them time. In my mind at the moment I wanted to help my Sector A CPC and be their handoff since they were the COMBINED position in the room and this maneuver can be difficult with ZZZ departures. He was handling it fine. I also began thinking of my plan with the controllers coming back. I wanted to relieve the trainee on Sector X quickly. They were only on for 30-40 minutes estimated at this time but because I knew she stopped talking I figured her exhaustion rate was high. I also was concerned the next controller to take the combined position was going to be a newer qualification who just returned from COVID and is more anxious to work combined. Person A began to speak on Sector X; he had a higher voice tone and used the word immediately so I knew something was occurring. Meanwhile; Sector Y next to them was handling a vast amount of IFR aircraft and Sector Z became saturated with the VFR straight ins along with IFR traffic. I continued to assist. When the next controller came in; the newer one; I warned him of the combined state and said I would assist him; he relieved the Sector A Controller and I used that same Controller to get out the training team after their incident. At the time I wasn't aware of the incident being a near mid air because nothing was said on the frequency. I believe it all occurred on Tower's frequency or was a ground complaint. After I relieved the training team; Person A did say something happened. Him being competent I knew he would do anything necessary in reporting he was already talking about it. I continued to work as promised I was the Sector A Controllers handoff during their busier traffic and I also ensured Sector Y and Sector A were slowing aircraft to 170 to help out Sector Z. I took more calls from the ZZZ Tower because they complained now Location another VFR entry was clouded and those aircraft must be a straight in as well. I informed the new Sector X controller. The first trainee came back early although not certified told him to scan the sector and speak up if hear anything unusual- I continued to be the handoff since I was certified. The Operations Manager then called and inquired about the near mid air. I asked what time and said Person A was working it. He and the trainee were still in the room at the time and they went to the front desk immediately. I continued to work CIC.ZZZ1 is a dangerous airport in my opinion. On a VFR day it is congested and on a marginal IFR day it is far more dangerous because the unpredictability of aircraft maneuvering clouds. My best recommendation for the airspace would be to have a corridor for both the arrivals and departures to protect the airlines on their inbound and outbound from the vast amount of training aircraft.For myself I did learn a lot from the incident. If I had more staffing I would assign a handoff as well as a trainer to the developmental. I also will be more vigilant in observing and reporting incidents. It was not my intention to not report it; I got distracted with many duties. I also think that me being a new CIC played a roll in hindsight perhaps getting the information and distributing that event has a higher priority- but I struggled to assist in helping the entire room with their live traffic at once. My mindset was to continue monitoring the active traffic since at this point afterwards it was still busy for many sectors.