Hello Nicolas,
Bellow you can find the bechmarks using `ffmpeg -benchmark` option.

1 - master

./ffmpeg -benchmark -t 10 -framerate 25 -f x11grab -i ":1+0,0 1920x1080"  
output1master.mp4
ffmpeg version N-109782-g458ae405ef Copyright (c) 2000-2023 the FFmpeg 
developers
  built with gcc 11 (Ubuntu 11.3.0-1ubuntu1~22.04)
  configuration: 
  libavutil      57. 44.100 / 57. 44.100
  libavcodec     59. 63.100 / 59. 63.100
  libavformat    59. 38.100 / 59. 38.100
  libavdevice    59.  8.101 / 59.  8.101
  libavfilter     8. 56.100 /  8. 56.100
  libswscale      6.  8.112 /  6.  8.112
  libswresample   4.  9.100 /  4.  9.100
[x11grab @ 0x564d03e165c0] Stream #0: not enough frames to estimate rate; 
consider increasing probesize
Input #0, x11grab, from ':1+0,0 1920x1080':
  Duration: N/A, start: 1675963927.428661, bitrate: 3379200 kb/s
  Stream #0:0: Video: rawvideo (BGR[0] / 0x524742), bgr0, 3520x1200, 3379200 
kb/s, 25 fps, 1000k tbr, 1000k tbn
Stream mapping:
  Stream #0:0 -> #0:0 (rawvideo (native) -> mpeg4 (native))
Press [q] to stop, [?] for help
Output #0, mp4, to 'output1master.mp4':
  Metadata:
    encoder         : Lavf59.38.100
  Stream #0:0: Video: mpeg4 (mp4v / 0x7634706D), yuv420p(tv, progressive), 
3520x1200, q=2-31, 200 kb/s, 25 fps, 12800 tbn
    Metadata:
      encoder         : Lavc59.63.100 mpeg4
    Side data:
      cpb: bitrate max/min/avg: 0/0/200000 buffer size: 0 vbv_delay: N/A
frame=  251 fps= 25 q=31.0 Lsize=    5720kB time=00:00:10.00 
bitrate=4686.0kbits/s speed=0.996x    
video:5718kB audio:0kB subtitle:0kB other streams:0kB global headers:0kB muxing 
overhead: 0.034719%
bench: utime=13.142s stime=0.307s rtime=10.039s
bench: maxrss=207576kB

2 - master

./ffmpeg -benchmark -t 10 -framerate 25 -f x11grab -window_id 0x5600008 -i 
":1+0,0 1920x1080"  output2master.mp4
ffmpeg version N-109782-g458ae405ef Copyright (c) 2000-2023 the FFmpeg 
developers
  built with gcc 11 (Ubuntu 11.3.0-1ubuntu1~22.04)
  configuration: 
  libavutil      57. 44.100 / 57. 44.100
  libavcodec     59. 63.100 / 59. 63.100
  libavformat    59. 38.100 / 59. 38.100
  libavdevice    59.  8.101 / 59.  8.101
  libavfilter     8. 56.100 /  8. 56.100
  libswscale      6.  8.112 /  6.  8.112
  libswresample   4.  9.100 /  4.  9.100
Input #0, x11grab, from ':1+0,0 1920x1080':
  Duration: N/A, start: 1675963986.581500, bitrate: 472305 kb/s
  Stream #0:0: Video: rawvideo (BGR[0] / 0x524742), bgr0, 841x702, 472305 kb/s, 
25 fps, 25 tbr, 1000k tbn
Stream mapping:
  Stream #0:0 -> #0:0 (rawvideo (native) -> mpeg4 (native))
Press [q] to stop, [?] for help
Output #0, mp4, to 'output2master.mp4':
  Metadata:
    encoder         : Lavf59.38.100
  Stream #0:0: Video: mpeg4 (mp4v / 0x7634706D), yuv420p(tv, progressive), 
841x702, q=2-31, 200 kb/s, 25 fps, 12800 tbn
    Metadata:
      encoder         : Lavc59.63.100 mpeg4
    Side data:
      cpb: bitrate max/min/avg: 0/0/200000 buffer size: 0 vbv_delay: N/A
frame=  250 fps= 25 q=31.0 Lsize=    1274kB time=00:00:09.96 
bitrate=1047.9kbits/s speed=   1x    
video:1272kB audio:0kB subtitle:0kB other streams:0kB global headers:0kB muxing 
overhead: 0.151768%
bench: utime=0.628s stime=1.465s rtime=9.920s
bench: maxrss=52268kB   


3 - patch applied

./ffmpeg -benchmark -t 10 -framerate 25 -f x11grab -i ":1+0,0 1920x1080"  
output1.mp4
ffmpeg version N-109783-g2352934f8b Copyright (c) 2000-2023 the FFmpeg 
developers
  built with gcc 11 (Ubuntu 11.3.0-1ubuntu1~22.04)
  configuration: 
  libavutil      57. 44.100 / 57. 44.100
  libavcodec     59. 63.100 / 59. 63.100
  libavformat    59. 38.100 / 59. 38.100
  libavdevice    59.  8.101 / 59.  8.101
  libavfilter     8. 56.100 /  8. 56.100
  libswscale      6.  8.112 /  6.  8.112
  libswresample   4.  9.100 /  4.  9.100
[x11grab @ 0x55e86905b5c0] Stream #0: not enough frames to estimate rate; 
consider increasing probesize
Input #0, x11grab, from ':1+0,0 1920x1080':
  Duration: N/A, start: 1675964519.431271, bitrate: 3379200 kb/s
  Stream #0:0: Video: rawvideo (BGR[0] / 0x524742), bgr0, 3520x1200, 3379200 
kb/s, 25 fps, 1000k tbr, 1000k tbn
Stream mapping:
  Stream #0:0 -> #0:0 (rawvideo (native) -> mpeg4 (native))
Press [q] to stop, [?] for help
Output #0, mp4, to 'output1.mp4':
  Metadata:
    encoder         : Lavf59.38.100
  Stream #0:0: Video: mpeg4 (mp4v / 0x7634706D), yuv420p(tv, progressive), 
3520x1200, q=2-31, 200 kb/s, 25 fps, 12800 tbn
    Metadata:
      encoder         : Lavc59.63.100 mpeg4
    Side data:
      cpb: bitrate max/min/avg: 0/0/200000 buffer size: 0 vbv_delay: N/A
frame=  250 fps= 25 q=31.0 Lsize=    5723kB time=00:00:09.96 
bitrate=4706.8kbits/s speed=0.996x    
video:5721kB audio:0kB subtitle:0kB other streams:0kB global headers:0kB muxing 
overhead: 0.034227%
bench: utime=14.005s stime=0.168s rtime=9.998s
bench: maxrss=207828kB


4 - patch applied


./ffmpeg -benchmark -t 10 -framerate 25 -f x11grab -window_id 0x5600008 -i 
":1+0,0 1920x1080"  output2.mp4
ffmpeg version N-109783-g2352934f8b Copyright (c) 2000-2023 the FFmpeg 
developers
  built with gcc 11 (Ubuntu 11.3.0-1ubuntu1~22.04)
  configuration: 
  libavutil      57. 44.100 / 57. 44.100
  libavcodec     59. 63.100 / 59. 63.100
  libavformat    59. 38.100 / 59. 38.100
  libavdevice    59.  8.101 / 59.  8.101
  libavfilter     8. 56.100 /  8. 56.100
  libswscale      6.  8.112 /  6.  8.112
  libswresample   4.  9.100 /  4.  9.100
Input #0, x11grab, from ':1+0,0 1920x1080':
  Duration: N/A, start: 1675964455.191272, bitrate: 472305 kb/s
  Stream #0:0: Video: rawvideo (BGR[0] / 0x524742), bgr0, 841x702, 472305 kb/s, 
25 fps, 24.83 tbr, 1000k tbn
Stream mapping:
  Stream #0:0 -> #0:0 (rawvideo (native) -> mpeg4 (native))
Press [q] to stop, [?] for help
Output #0, mp4, to 'output2.mp4':
  Metadata:
    encoder         : Lavf59.38.100
  Stream #0:0: Video: mpeg4 (mp4v / 0x7634706D), yuv420p(tv, progressive), 
841x702, q=2-31, 200 kb/s, 24.83 fps, 19072 tbn
    Metadata:
      encoder         : Lavc59.63.100 mpeg4
    Side data:
      cpb: bitrate max/min/avg: 0/0/200000 buffer size: 0 vbv_delay: N/A
frame=  250 fps= 25 q=31.0 Lsize=     961kB time=00:00:10.02 bitrate= 
785.0kbits/s speed=1.01x    
video:959kB audio:0kB subtitle:0kB other streams:0kB global headers:0kB muxing 
overhead: 0.199722%
bench: utime=1.624s stime=0.049s rtime=9.920s
bench: maxrss=51996kB

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