The big tech AI barons absolutely claim that their LLMs can replace educators, judges, lawyers, and personal trainers. I've seen some vague claims about childcare robots, but for whatever reasons anything that's not pure software appears to be currently outside their field of vision. They're unlikely to make any claims about social workers because there's not enough money in it.

No; the services that seem most intractably human, at least given the current state of things, are very much those in personal care roles—nurses, elder care workers, similar sorts of on-the-ground, in-person medical/emotional care—and trades, like plumbing, construction, electrical work, handcrafts, etc.

Until we start seeing high-quality general-purpose robots (whether they're humanoid or not), those seem likely to be the jobs safest from direct attempts to replace them with LLMs. That doesn't mean they'll be safe from the overall economic fallout, of course, nor that the attempts to replace knowledge work of all types will actually succeed in a meaningful way.