IMHO a very capable FOSS competitor for Obsidian is LogSeq (https://logseq.com/). I use Logseq since 6 month and love it. There also exists a Kanban Plugin for LogSeq, which I have not yet tried... https://github.com/hkgnp/logseq-kanban-plugin

Looks Nice! Also interesting to see they are incorporated. Would be cool to watch how they evolve the product while also implementing a business plan.

But from the home page I don't directly get whether this is backed by markdown flat files or some other system, do you know?

Its local markdown flat files.

LogSeq has suffered a lot, imo, since they took venture funding. Their focus has wavered drastically since then, shipping features nobody is asking for that I can only assume are viewed to be differentiating for other PKMs (e.g., canvas) vs making the thing performant, improving the wretched UI, fixing bugs, etc.

Obsidian may not be open source, but it reflects a sane approach to product: small, focused team, profitable company, delivering useful stuff. Clean and tight. It's got a different set of abstractions at its core (document model vs block model) but if you're indifferent to that, Obsidian is where I'd start.