New bed
For peace of mind, I ordered a spare cover, because I had sewn the furry blanket from the original cover firmly onto the cover (see references, it’s supposed to be attached with Velcro, but that doesn’t even last a minute). Just washing the blanket makes no sense, i.e. it comes off right away and then everything gets cleaned.
This spare cover is made of much sturdier material! I basically have a brand new dog bed! Highly recommended! With this cover, I also sewed the furry blanket onto the bed cover again.