This is undocumented (frustrating) but it looks like it's chunking them, running embeddings on the chunks and storing the results in a https://qdrant.tech/ vector database.
Interestingly, when I used an .md extension, GPT would write python code to try to pull parts out to answer queries (which worked miserably), but when I used .txt (for the same files), it seemed to put it in the vector store.
I've had good success putting code examples in a single txt file for our custom framework, and it seems to use that neatly for generating code. I'm surprised you've not had much success with them, I gave an assistant my wife's PhD thesis and while the API was working initially it seemed alright.
Does that error message really confirm qdrant for Chat? It's just failing to index a file called 'qdrant', and I don't see any further proof offered in that thread.
We know it's Qdrant because an error message leaked that detail: https://twitter.com/altryne/status/1721989500291989585
It only applies that mechanism to some file types though - PDFs and .md files for example.
Other file formats that you upload are stored and made available to Code Interpreter but are not embedded for vector search.