I want sound on both PC speakers and TV speakers
Then you are going to want to split the audio signal going to the PC speakers and send those over to the TV.
I've helped a few with getting PC speakers and audio over HDMI at the same time but folk don't seem to understand why that's a bad idea. It's pretty simple as each method of transport has a different delay and that delay changes from system to system so you get this ball park echo issue.
Those new to this might ask "I thought they solved that?" To which I ask them about their last ball park experience. Yup, still an issue.
If you split the signal and send it analog then there is no such effect.