You tried encoding with your iGPU but 6th gen & older are no longer supported by OBS. I'm not sure if you're going to be able to get any traction with your AMD GPU either, but give it a shot. Might need to update the drivers.
09:30:03.492: [qsv encoder: 'simple_video_stream'] settings:
09:30:03.492: codec: H.264
09:30:03.492: rate_control: CBR
09:30:03.492: target_bitrate: 6000
09:30:03.492: Lookahead Depth:60
09:30:03.492: target_usage: TU4
09:30:03.492: profile: high
09:30:03.492: keyint: 2
09:30:03.492: latency: normal
09:30:03.492: b-frames: 3
09:30:03.492: fps_num: 60
09:30:03.492: fps_den: 1
09:30:03.492: width: 1280
09:30:03.492: height: 720
09:30:03.492: [qsv encoder: 'simple_video_stream'] debug info:
09:30:03.504: [qsv encoder: 'msdk_impl'] Specified object/item/sync point not found. (MFX_ERR_NOT_FOUND)
09:30:03.504: [qsv encoder: 'simple_video_stream'] qsv failed to load
09:30:03.504: major: 1
09:30:03.504: minor: 0
09:30:03.504: Stream output type 'rtmp_output' failed to start!
If the AMD encoder fails too, you'll have to use x264 or you can roll back to OBS 27.2.4. It's the last version that supports the older hardware.
Also, turn HDR off on your TV. The 12-bit > 8-bit color conversion is un-necessary & only adding load to the system.
09:29:51.787: name=Digital TV
09:29:51.787: pos={0, 0}
09:29:51.787: size={1920, 1080}
09:29:51.787: attached=true
09:29:51.787: refresh=59
09:29:51.787: bits_per_color=12
OBS Studio - Free and open source software for live streaming and screen recording - obsproject/obs-studio
github.com