It would also be a plain and simple category error. The legal code is not concerned with the how. It doesn't list actions but abstract pursuits, outcomes. "Open source development" simply doesn't fit there. My previous comparison was "cleaning toilets". It can equally be part of a charitable activity beneficial to the public if you do it for a charity, yet there would be no point in adding it to a closed list.
By the way, it would still require the project to register as a German charity, file reports, etc.
Plenty of questions, zero answers in the petition. The petition doesn't state what their goal is at all. What is the actionable item, what is the request, and from whom? Even a prayer is usually more specific.
To me, it doesn't read at all like the petition is advocating to add "open source" to the list of charity goals, since that has nothing to do with "getting volunteering recognized" (whatever that may refer to). Charities work with money, which is what the law is about after all -- it's a Tax Code! All it deals with is money. Unless you deal with actual financial flows, you don't need to respect any of that, and you're free to do whatever! "Volunteering" has very little to do with money.
And I say that as somebody who has almost exclusively worked for and with charities, in both paid positions and as volunteer, for the past decades. I really don't know what this is advocating for. I get a lot of "recognition" for my contributions to open source projects, both finanicially and non-financially, and so do others that I know who contribute to open source.
It's like petitioning for "rainbow cotton candy". Sounds nice -- who would object to that! But: Who? What? Where? How?