You can download [1] the latest release of open3a to find not only the PHP source code, but also an AGPL license. This isn't open contribution software (no public Gitlab project to do pull requests and such) but the source code itself seems perfectly open source.
Even still, open source licenses may be used to sell software for which the source code is not available before purchase. For example, the Apache 2.0 license can be used for this; it protects users of altered versions of the source code from patent infringement lawsuits and forces the Apache license to be passed on to the end users of the modified work. It doesn't forbid throwing the source onto a repository somewhere, of course, so the source doesn't remain closed for long, but I can imagine many businesses wouldn't want to sell their technical support to a company that published their source code, and businesses are generally wary of using software without any form of support.
There's various ways people use the term "open source" and I think in general people mean "software that's available publicly for free" when they use it, but some of the open source licenses allow for some propietary-like behaviour while using them.
What's to prevent someone from putting it up on GitHub? Of course the customers are buying support too, and OP could probably make a copyright takedown if the name and logos are used as-is, but it sounds somewhat risky. There again I haven't built a successful business like this, so what do I know :-)
Very little, indeed. However, just a blob of source without any updates or progress isn't very useful. I doubt many companies will buy software and take it upon themselves to maintain a public repository of someone else's source code. There's no profit to be made in that.
The copyright itself couldn't be used to take the code down, because the open license allows the customer to do exactly that.
Theoretically, a customer can buy the software, fork it, and turn it into an open source fork. Without the support contract to receive updates, though, I doubt that'll be very useful in the end.
At worst, a competitor buys your software and uses your own software against you by analysing, publishing and extending it, and selling support contracts in your market. However, I strongly doubt there's much money to be made that way.
I'm no businessman either so I wouldn't know what brings companies to make software like that. I think these licenses were born in an era of offline, compiled blobs that received updates every month at the most, whereas modern software development is much more focused on freemium and SaaS.
Even still, open source licenses may be used to sell software for which the source code is not available before purchase. For example, the Apache 2.0 license can be used for this; it protects users of altered versions of the source code from patent infringement lawsuits and forces the Apache license to be passed on to the end users of the modified work. It doesn't forbid throwing the source onto a repository somewhere, of course, so the source doesn't remain closed for long, but I can imagine many businesses wouldn't want to sell their technical support to a company that published their source code, and businesses are generally wary of using software without any form of support.
There's various ways people use the term "open source" and I think in general people mean "software that's available publicly for free" when they use it, but some of the open source licenses allow for some propietary-like behaviour while using them.
[1]: https://www.open3a.de/page-Download