How do you (or your company) retrain staff for new roles?

Hive mind: Does your company re-train people to teach them new skills? What about mindset skills, such as problem-solving and critical thinking? What's worked -- and what doesn't?

I'm writing an article on how to do effectively re-train workers, and I'd like to hear from you (particularly if you have a management or HR background). I might like to quote you, but I certainly would like your input even if that isn't possible.

Companies have always needed to ensure their employee learn new tools (such as replacing OldProgrammingLanguage with NewLanguage) or entirely new skill sets (e.g. for those whose jobs are replaced by automation). But the rate at which old skills perish and new ones have to be learned is increasing.

If we assume that technology changes jobs rather than destroys them, what does that mean for companies in practice?

I was inspired to write this article after reading about “the work skills of tomorrow" https://www.weforum.org/agenda/2020/10/top-10-work-skills-of-tomorrow-how-long-it-takes-to-learn-them in which critical thinking and problem-solving top the list of skills employers believe will grow in prominence. But that made me wonder: How the heck do you teach soft skills? This isn’t like telling someone, “Take a course in data analytics.” What, if anything, can you do to improve a worker's agility in learning new things, or to become a better problem-solver?

So: What has been your experience? What worked, what failed, what advice would you offer someone (particularly in larger organizations) who wants to take care of their people and move the company forward?

Note that I'm thinking less in terms of training an individual with a new skill (PhotoShop) than skills for a different career (a move to the Accounting department). And please leave out the "I trained myself!" stories; they're a tangent that doesn't help me. And yes, I know plenty of companies just lay people off rather than retrain them; we can leave those out of the discussion, too. This is meant to be a useful how-to to guide companies that want to do it right, so I am interested in practical advice.

We can take this to a private discussion if that's easier.