Update from beta to 3.0.0 leads to entity/fields definition errors

Which beta version? Did you update the Registration module and Drupal Commerce at the same time? The errors on the Order entity are with Drupal Commerce and not related to Commerce Registration. It makes me think you may have a general issue with Drupal Commerce order objects in your install, and not an issue with Commerce Registration.

It was the beta4 version.

I did a composer update so Drupal Commerce could have been updated at the same time, indeed.

It's the first time I'm experiencing this error, but you're right, it's probably coming from the Commerce side instead.

Instead of doing a general composer update, try this:

composer update drupal/registration drupal/commerce_registration -W

That will update only the registration related modules, and not Commerce, which may help.

(You would have to restore your DEV site from backup first, of course, before trying this approach.)