Streamlit sharing has supported Git LFS since February of this year. I will find out from the team if there’s a max file size after which the file is not detected.
In the meantime, note that there are resource limits 3 on sharing:

You can deploy up to 3 apps per account.
Apps get up to 1 CPU, 800 MB of RAM, and 800 MB of dedicated storage in a shared execution environment.
Apps do not have access to a GPU.

Large models such a BERT-base will not fit in memory. You may be able to load distilled or quantized versions of those models, depending on their size and support for inference on CPU.