Does streaming with a DSLR cause lens/sensor damage?

Generally, no, you won't cause any harm to your camera. Some older (like a decade+) cameras were susceptible to long term harm due to heat management issues, but even those were usually specific to recording in unfavorable (heat wise) conditions like outdoors under direct sunlight.

Your T6 is just fine to use as a face cam, even under long hours, under most indoor conditions. It's always a good idea for people interested in using live view mode for long periods of time to search for heat management issues specific to their model. As mentioned above, there ARE some older cameras that do have heat management issues capable of damaging sensors. Though even then it wasn't a widespread problem.

/r/Twitch Thread