Anecdotally I've heard from my biochem circle of friends, that many institutions (at least in Germany) are still quite particular when it comes to lab notebooks. Especially ones that strongly monetize on patents, e.g. Frauenhofer. They usually also provide electronic lab notebooks which can either be used directly or into which you have to store copies of the original physical lab notebook.

I suspect that this may be due to different copyright mechanisms in different jurisdictions. e.g. in Germany employees have stronger protections that may allow them to still patent stuff developed in their free time, so companies might want to have a stronger papertrail to prove that outcomes tie back to something done during working hours.