There is sadly no hdmi CEC support on Most GPUs for pcs. So when you want your tv to turn on and off with your pc it is only possible with the tv being reachable from your pc via ip.
I believe LG doesn’t advertise such an api via Bluetooth
HDMI breakout and a esp32 module flashed with esphome is another option. The tv most likely doesn’t care that the port that sent on/off command is not the same port the video signal is coming from..
You can get USB controlled CEC injectors for HDMI.
https://www.pulse-eight.com/p/104/usb-hdmi-cec-adapter