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Are you using discrete GPU mode? You should check what GPU is connected to your HDMI port. I know that on some systems (e.g. my Legion), if you use discrete GPU mode and your HDMI port is only connected to GPU1, then Xorg defaults to using GPU0 and therefore would not display anything through the HDMI. If this is your case, then try disabling discrete GPU in your BIOS setting (or through vendor software on Windows, if you dual-boot) in place of integrated/dynamic GPU or whatever option so that your system only discovers one GPU, which forces both XOrg to choose that one. In addition, you might also be able to tell XOrg to use GPU1 through conf files, but I'm not familiar with that and it's something you may have to look into.