https://huggingface.co/BAAI/bge-base-en-v1.5
is described as an "LLM" by the people who created it. It can be used in the SBERT framework.
I tried quite a few models for my RSS feed recommender (applied after taking the embedding) and SVM came out ahead of everything else. Maybe with parameter tuning XGBoost would do better but it was not a winner for me.
If you look at the literature
https://arxiv.org/abs/2405.00704
you find that the fashionable LLMs are not world-beating at many tasks and actually you can do very well at sentiment analysis applying the LSTM to unpooled BERT output.