I’m having the same problem.
Not sure if this has anything to do with it, but my issue, same as OP’s, was instantiated after installing PostgreSQL within my local repo. I had to delete my former, working, local repo and git clone my app from Heroku to try and start from scratch; however, ‘pg’ was still a dependency listed in my package.json, even though I had never pushed to my Heroku git branch after installing PostgreSQL (this is a separate issue, I digress…).
Anyway, I have a working Heroku app in production and haven’t pushed my local repo to that one because of having the same problem as OP’s. I.e., I’m receiving an “Internal Server Error, must supply api_key…” when trying to upload an image/asset during development. It seems as though all my cloudinary environment variables are setup correctly both in my code and on Heroku. So I’m at a loss right now. Did you or anyone ever come up with a solution?