:AIChat hangs and has no output for higher number of tokens

[Konfekt]

I did not pinpoint the exact number of tokens passed, but for example for a visual selection of 800 lines with < 6k words, :'<,'>AIChat /role hangs for a few minutes and then shows no output on Vim 9.1.919 on Ubuntu 22.04.
Using e.g. an OpenAI model this should still be below theirs maximal number of tokens (around 200k for some models).