What do think about a common consciousness among several Tesla bots, cars and the home?
Consciousness is maybe not the right word, but the "brain-software" will most likely be shared, yes.
If you haven't seen it, check out this
Lex Fridman interview with Rohid Prasad. Co-creator of Alexa.
All of it is worthwile to listen to, but specific to your question, listen from 29:50 onward. Alexa is one "AI" that has multiple embodiments of different kinds. This way Alexa is everywhere at once, and can be trained this way.
Current FSD beta is not entirely similar since it has local software and the learning happens at Tesla headquarters but needs to be pushed out to the fleet with OTA updates. Alexa on the other hand is online (lives in the cloud) and therefore the training happens simultaneously.
Similar concepts, but one more direct than the other. [EDIT: Alexa might be trained in a similar manner than FSD but you don't "update" Alexa, you always have the newest version available since you're connected to the internet. Still different than FSD beta.]
Either way, the future is not hard to imagine: Tesla AI will power your car, your energy generation/storage/sales to the grid, your HVAC, your multimedia devices (Tesla App Store, games and services, anyone? Could be streamed to your TV maybe), and most importantly your Tesla bot (house servant or romantic partner? You decide
).
That's why Elon often says "people will think of Tesla as an AI company more than a car company". I can imagine this to be true in about 10 to 15 years.