There are some labeled data (about 50-80 labeled documents per category. not 500 per category), so a few-shot learning might be an option.

Algorithms used: it might be something like KNearestNeighbor or some ML/Neural networks (transformers? LLM?). Should just do the proper classification.

Some restrictions: It should be a "ready to use" pipeline with documentation about training the model, parameter optimization etc. If possible - there should be some way to use this framework/library without Python (I'm not a Python developer) For example, the [1] and [2] allow to use command-line interface for everything - it seems using Python is optional for these frameworks. The SetFit framework (see [3] and [4]) looks quite promising (good results with 8 labeled samples per class!). But requires doing everything in Python.

[1] https://fasttext.cc/docs/en/supervised-tutorial.html

[2] https://neuml.github.io/txtai/pipeline/text/labels/

[3] https://github.com/huggingface/setfit

[4] https://www.philschmid.de/getting-started-setfit