In my experience, DWC systems support plants fine without the pumps. I used them for years before trying Kratky, and sure enough, the plants still grow. This might vary by species. I have had pump failures as well, but never more than 36 hours or so. In any case, it wasn't enough to harm the plants.
An aside: I just looked up Kratky (to be sure I had the name right) and the image results are pure insanity. AI generated nonsense. There's one where the image generator used perfectly clear containers and included some sliced limes in the media, haha. And soil.
Starting a hobby like hydroponics will probably be so confusing with garbage like this all over the place.
edit: The lime-aid dirty Kratky system
https://easyhomehydroponics.com/wp-content/uploads/2024/09/c...