It's true that there are plenty of cooperatives and employee-owned businesses, but that doesn't make them common. Today there are roughly 6,322 employee owned companies in the US. There are 1,030 in the UK. And as I show in this post, there are only 11.1 million worker-owners globally, out of 3.39 billion total workers—that’s only 0.33% of the working population. Very miniscule.
General partnerships are interesting, but that doesn't mean they provide equity to employees. There are certainly prominent tech companies that do, and you're right that it would be great if we could include some of those in our stats—I'll look into that. Still, most equity packages are reserved for senior employees, not all employees. And at private companies most employees won't see the benefits of that equity unless the company sells or goes public so it's kind of imaginary until then. But you are very right that it's a segment worth investigating.
I think that General Partnerships are easily overlooked as a model of employee ownership. Alone in the US there are approximately 450.000 law firms (and then there are also all the accounting, finance and medical parctices structured like this).
With law firms, they are actually required by law to be partnerships, as they can only be owned by lawyers, so there can be no outside investors. It even goes further than this, in that in most firms only practicing lawyers can be partners, so if you stop working you have to transition to an "in counsel" role, where you no longer have ownership.
Ironically, this is probably the most anti-capitalist model you can think of, in that only actual workers can be owners, with no room for participants that only offer capital.
This model is easily overlooked, since it can seem a bit elitist, being mostly used in the highest earning segment of business, and also because partnership is rarely extended to all employees (it would be a rare firm where even the receptionist was a partner as well). But there is no intrinsic reason that this couldn't be the case.
It is an interesting model because it has a long history and all the legal infrastructure in place. Almost every country allow general partnerships or something very similar. And in contrast with cooperatives, it has no problems attracting very highly skilled employees.