> Organisations who actively pay for trainings are rare.

Maybe this depends on region? I've worked at 5 different companies in the EU, and every one of them reimbursed pretty much any kind of training I wanted (including physical courses, conferences, online courses and books). In fact, I regularly see software dev job ads that list a personal development budget as a benefit.

Perhaps it's related to some EU employment law about "career progression"?

Every contract I've signed certainly had such things in there.

Often employers say they'll pay for exams but not allocate study time during your working week.

I’m not sure how it is now, but in Australia a while ago, I’d you wanted to import workers because you couldn’t source talent locally, you also had to train your local staff to justify visas

Anything really? Say you work as backend developer, would they pay a training on machine learning or computer vision?

I worked as a backend developer and got reimbursed for both a JS course and a machine learning course. As long as you can provide a plausible reason why it makes you more effective, managers are usually more than happy to sign off on it. In this case it was pretty straightforward to come up with a good story on how understanding adjacent product development areas would make me a more effective dev.