Mmmmh, well according to the log there's absolutely nothing wrong and the transponder was set. So, if you're not seeing it being set then it must be the aircraft, although PF3 can actually read it too because it frequently checks to ensure the transponder is set correctly throughout your flight.
11/26/2023 2:21:01 PM: 480 - Transcript: 'Roger QNH 1014 Ground on 118.5 Condor 8632 '
11/26/2023 2:21:01 PM: 480 - FS Screen : Roger QNH 1014 Ground on 118.5 Condor 8632
11/26/2023 2:21:08 PM: 570 - COM Freq changed to: 118.5 IPC Set: 6224
11/26/2023 2:21:08 PM: 570 - COM Changes at #2
11/26/2023 2:21:09 PM: 570 - Send to PF3 Display - 1:2:118.5:0:0:0:0:
11/26/2023 2:21:10 PM: 590 - Calling Trans_Freq...
11/26/2023 2:21:10 PM: 590 - Write to FSUIPC 26471
11/26/2023 2:21:10 PM: 590 - FSUIPC RetCode: 0
11/26/2023 2:21:10 PM: 590 - Trans_Freq Returned...
11/26/2023 2:21:10 PM: 590 - Transponder changed to 6767 at #1
11/26/2023 2:21:10 PM: 590 - LX:7000, CX:6767, XSet:1, iX:6767
11/26/2023 2:21:10 PM: 590 - TRANSPONDER Correct!