A corporate jet Captain reported the aircraft was unable to reach its assigned altitude and began a descent into a confliction with another aircraft below it.

Narrative

As the PIC of Aircraft X operating from ZZZ to MBPV on this day; in an effort to save fuel whilst assessing metrological conditions my Second in Command (SIC) and I made the call to request a cruise altitude of FL430. While in the climb and approaching FL429; we started to notice that the ISA drop was not what was expected based off of interpolation and realized very quickly that the aircraft would be very sluggish to perform at the altitude requested. Soon after that realization the aircraft began to buffet (no stick shaker or pusher was presented) however; the quick onset of the buffet began to make the autopilot fluctuate in an effort to maintain the altitude entered. I immediately asked for a lower altitude explaining that we were unable to maintain the altitude to which a frequency change was given to us in response. Still seeing the trend start to worsen and the buffets become larger I took it upon myself as the PIC to prevent a stall scenario. Disconnecting the autopilot to start a slow descent to regain the airspeed and was met with a faster than expected descent rate. Before I was able to rectify the drop in altitude; we were given 50 degrees right turn by the Center Controller and I saw my lowest point to be 41700ft which triggered a Level Off RA from My TCAS. I had the oncoming aircraft insight under the VMC condition and I a rectified my altitude loss climbing up to 42000 feet where I could maintain the aircraft free of any stall condition for the time being. There were no injuried aboard.