It's served from the cloud but it runs entirely on your PC (except the AI generative tools). It can't run entirely offline though, because the js, webassembly, and assets are served chunked as-needed.
Saying Photopea is good enough is really underselling it. It's so far ahead of anything offered by the open-source community.
I'd be so happy to pay for a fully offline version of Photopea!
Off topic, but there is something like that: photopea, it's free and it's good enough for my use cases (I need it once a year maybe).