Sorry the OP is somewhat ambiguous. I thought you were trying to cover up the sound of a TV from people who are sleeping (or possibly vice-versa).
Just so we’re all completely clear, you are attempting to cover up your own sounds from other people who are sleeping, and you will use the TV as the white noise output device, correct?
I think just simple static white noise should be sufficient. We have an air purifier running in our bedroom and the sound of that fan pretty much annihilates all other sound. Mouse clicks and doors opening and shutting are very sharp noises, but are still relatively quiet, and as long as the source of the white noise is closer to the sleeping people than your noise you should be fine, if that makes sense.
I’ve got ringing in the ears, so I like a clock ticking or water dripping. And I used to use an off-station radio to cover office noise.
But if you want to cover noise, “white” noise isn’t the best. It puts out energy where it’s not needed, which means that it’s louder to cover the sounds, which means it’s loud enough to bother people if it has to give solid coverage. So pink noise is better.
But noise isn’t just about volume, it’s also the brain paying attention to things that might be important. So you want to mask dynamic changes as well constant noise. To do that, you want, in increasing order of specialization, rain noise, ocean noise, babble noise.
Rain noise and ocean noise are the most famous sleeping noises. Babble noise (brook babbling or people babbling) is more intrusive, but gives better coverage. If you need to cover an actual busy noisy environment, the last two are what you go for.