Realistically, I see the initial tesla bot as being very limited. Right now, the Tesla Bot does not even exist. It could take years to make it to actual production and something practical. Also, Elon's claims that they can just use all they've learned from FSD is BS. They are completely different applications. They would need to train the bot vision for navigating say inside a person's house which would require tons of data. You would need to train the vision for different types of floors, all types of furniture etc... Navigating inside a house is very different than driving on the road. And everybody's house is different. Some people leave stuff on the floor that the bot could trip over if vision does not recognize it. I think it will take a while before the bot would be any good. It will likely be "beta" and require supervision like FSD Beta does.
But speculating:
It could be a walking "voice assistant" like Siri or Alexa where it can respond to voice queries. You could summon it with "Tesla Bot, come to me" and the Tesla Bot would walk up to you. Then you say "TeslaBot, what will the weather be like tomorrow?" and the TeslaBot does a google search for your location and responded "The weather tomorrow will be sunny and 85 degrees". It could also make reservations for you. So you say "Tesla bot, make dinner reservations for 2 at La Cantina for tomorrow at 6pm" and the Tesla Bot goes to the website for La Cantina and places the reservation and says "I have confirmed your reservation".
I could also see the Telsa Bot carrying objects for you. So you say "Tesla Bot, take the package on the table and take it to my bedroom" and the Tesla Bot walks to the table, identifies a package with vision, picks up, takes it to your bedroom and drops it on the bed or night stand".