Offline-first can be a lot, from my perspective. Just as yours and David’s example, an application that work without active internet connection is valid. But this is rather common and the classic way how applications just operated for a long time (despite the modern mobile apps, which have to pull some strings nowadays to allow offline access).
What I find more interesting is when a system or application overcomes the otherwise required network connection. So maybe offpunk (from above) is an example, A web browser which puts everything in a cache, so you can continue to read, if offline. But that’s a rather simple approach as well. The whole “opportunistic syncing” approach by Syncthing is also matching. It also covers some ground regarding resiliency. So another aspect could be resilience, meaning a connected system will not just survive a temporary outage of a node, but also continues to work as expected. Many distributed tools would probably count, even classics like git. ActivityPub based tools and the fediverse, on the other hand, are somewhat resilient, but not offline-first. Scuttlebutt would be though: https://scuttlebutt.nz/
Back to your examples: I think if a “simple local application” would do something we usually use network for, but technically don’t have to, this would also be interesting for me. An actual example might be: https://devtoys.app/
I got recently inspired by this, which also has its own definition of offline-first: https://gemini.tildeverse.org/?gemini://zaibatsu.circumlunar.space/~solderpunk/gemlog/announcing-offlfirsoch-2025.gmi (proxied from the Gemspace)
Sounds super cool, but still don’t know what bonfire does in practical terms. Can anyone elaborate?