ESH (but mostly you; some fault with the housekeeper for how she handled it)

(I'm a hotel owner)

Cleaning is part of the housekeeper's job. But the core part of the job is normal cleaning. Hoovering, changing bedsheets, cleaning and sanitising surfaces and touch points.

Especially in this time of a global health crisis, vomit can legitimately be considered a biohazard, and requires extra PPE in any clean-up, (exception if the person cleaning up is going to be in intimate contact with the sick person anyway).

otoh, the housekeeper (and every customer-facing worker) is the face of the hotel. I would expect staff in this situation to provide the tools for the guest to clean it up themselves, and to make sure the guests know a "deep clean/damages" fee would be charged if they choose to leave the vomit for the hotel staff to clean. I would not expect staff to pull a face and give an "eww gross" reaction.

Consider that if you throw up in a taxi, you can typically be charged USD 50-100 automatically, depending on the city. It is quite unreasonable to expect staff to clean vomit without exceptional consideration.