Dead Cells has a Daily Challenge or Daily Run mode, but it is just a minor optional part. Except that is required in order to unlock three weapons (“blueprints”) for the main game. Just by starting a Daily Run on different days unlocks the following blueprints:
However, specifically the Linux version on GOG has an issue where it is impossible to start the Daily Challenge. The Linux version on Steam is not affected. To use anything online-related in Dead Cells – which thankfully is not a lot as it is a local single-player game – the GOG GALAXY client is required. Which does not exist for Linux. Until a GOG GALAXY client for Linux is released, I probably should not buy games from GOG anymore and just go with Steam, because otherwise I cannot trust that all features
The Dead Cells issue is known for years and by now it seems rather unlikely it will be fixed. At some point a note was added to the store page: