Metacam is a brand name for the drug meloxicam. Meloxicam injectable is commonly given to both dogs and cats post surgery for pain relief. Metacam itself is now available in a form suitable for cats.
Convenia on the other hand I have very little knowledge about so I won't pretend that I do. It has apparently been approved for use in both dogs and cats, so I would assume that your vet gave the correct dosage as per weight.
Your vet sounds like they were very thorough performing a preanaesthetic blood test and probably would not have given any drugs without prethought. If you are unhappy, talk to your vet about it and ask why it was given and maybe even the possibility of giving your cat the antibiotics yourself in future?
I hope your cat is doing better.