I’ve seen this done as a carve-out or exception that has to be explicitly documented. Trouble is that documentation is not presented as simple.

Yes, but you have to declare them to the company and the company must approve them. If they don’t, because it’s competitive, you’re out of luck.

This is also something I try to ask for - generally I get the "that's fine" from the hiring manager and HR, but both times I've then had to push back and get it added to the actual supplied contract. And that was very much not easy.

And even then there's normally a "Sufficiently Different Sector" requirement for those personal projects - which makes sense, but it is inevitably worded vague enough that it would likely require going to court for pretty much any project to show it's not directly related. And that would be near prohibitively expensive for me as an individual if the relationship actually became adversarial.