However, in my experience it's haphazardly enforced. If you're on good terms with a colleague or manager, it's my understanding (IANAL) that they can still provide an informal or personal reference. In practice, for most prospective employers this is just as good as a formal reference (since most companies these days have the aforementioned policy anyways).
In my experience, although near-ubiquitous a no-reference policy mostly seems to mean "if anyone calls the company line or shows up on prem, we redirect them to HR who then tells them nothing". It doesn't mean they go out of their way to stop individual employees from giving positive references on their own time (to wit I've never seen any employer actually make any effort whatsoever to disseminate their no-reference policy to employees, it's just a CYA measure they adopt if communication happens through channels they're directly accountable for)
I guess it's just another sign of corporate hypocrisy - please provide references when applying, but we will not allow you a reference when leaving.
And sometimes this works. If you are (to take an extreme example) Linus Torvald and your open source project in Linux, then holy cow, I'm gonna hire you right away. But most people don't have the combination of talent, luck and perseverance that are required to get wide adoption of an open source project. So in 99% of cases, what you are left with is a library or small project that you threw up on a git-hub that maybe has a few stars and that almost no one uses.
Furthermore, as a hiring decision maker, I really don't have much time to actually read your code. Got a project with 3 stars on github? That's great, but I'm really pretty busy writing new features and maintaining my code and I don't have time to read through your code unless I'm pretty certain I'm going to hire you, so I look for proxies. Number of stars is one of them. If 1000 people use your product, it probably says something about the quality of your code or the difficulty of the problem you solved, or at least your ability to solve a problem in a way that people find useful (yes, yes... I know it doesn't guarantee any of these are true, it's just a proxy, but in the initial stage of interviews, proxies are useful).
The issue is that most people are never going to write a project from scratch that gets 1000 stars. However, if you have substantial work in a project that you didn't start, that's also a great proxy. This means that you collaborate with others and not only that, but the people you collaborate with think you are good enough that they are willing to merge in your code. That's a good proxy.
As a filter for useful, sharable code, open-source is an almost total failure?
That said I haven't really solicited advice on either. My concern is more specifically related to how to frame my past employment and medical issues for a future employer - not so much making it through a technical screening.
I was, and am, curious about what others deem important to their career and craft (e.g. fundamentals), but like I said it's mainly curiosity. If you have something to share I'm all ears, and if not I wish you well.
Brush up on the fundamentals. Maybe read cracking the coding interview. And if possible, spend some time working on an open source project, preferably an existing one, not your own (it shows you can collaborate, which is a useful skill if I'm gonna hire you).