>they've solved reinforcement learning?

Transformers can do Reinforcement Learning yes.

https://arxiv.org/abs/2106.01345

https://arxiv.org/abs/2205.14953

>they can handle continuous domains, like robot motion?

Yes they can handle it just fine. Excellently in fact.

https://www.deepmind.com/blog/scaling-up-learning-across-man...

https://tidybot.cs.princeton.edu/

https://general-pattern-machines.github.io/

https://wayve.ai/thinking/lingo-natural-language-autonomous-...

I don't know if anyone is saying they're the best at or have "solved" everything but they can damn near do anything.