I can see one way that the first option would work. Back in the 1980s, the UK had a similar thing for artists, where they weren't required to produce specific works for the government, or were controlled by the government in any way. They just got the money so they could produce art. While there were definitely some abuses of the system, entirely because the government weren't really checking in on what anyone was doing with the money they got, it also led to a lot of successful artists who otherwise wouldn't have had the opportunity to just work on art, particularly working class artists. It's genuinely one of very few things the Thatcher government did that made the world better.

I'm very much a proponent of such a system existing again in the future. Essentially some form of unconditional income support for creatives, under the notion that their work is a social good that shouldn't be constricted by commercial incentives. I see no reason why that shouldn't apply to open source developers, since their work also benefits society as a whole. As long as the government remains hands-off in regards to what is made, and gains no rights to the work (ensuring that the open source software remains open source), it would in theory be more effective than relying on donations from the private sector. I suppose it still violates the spirit of open source, but it's also a model that has been successively used to support artists, who often share that "the big man can't control me" political leaning.