[DOCS] pip install litellm missing proxy extras — fails at runtime after 45-min model download

[dims]

Summary

The Brev model-serving guides instruct users to run pip install litellm. This installs the SDK but not the proxy dependencies. Running litellm as a server then fails with:

ImportError: Missing dependency No module named 'backoff'.
Run `pip install 'litellm[proxy]'`

This error surfaces after the model has already downloaded (~45 minutes for an 80 GB model), making it feel like a fresh blocker at the worst possible moment.

There is a second issue on Ubuntu (the default Brev instance OS): pip install places executables in ~/.local/bin, which is not in the default PATH. Running litellm immediately after install produces command not found.

Steps to reproduce

1. Follow any Brev model-serving guide that includes pip install litellm
2. Wait for model download to complete
3. Run litellm --model openai/... --api_base http://localhost:8000/v1 --port 4000
4. See ImportError: No module named 'backoff'

Expected behavior

The documented install command produces a fully functional litellm CLI.

Correct install and start sequence

pip install 'litellm[proxy]'          # NOT pip install litellm
export PATH="$HOME/.local/bin:$PATH"  # ~/.local/bin not in PATH by default on Ubuntu
export OPENAI_API_KEY=dummy           # litellm requires this even for local endpoints
nohup litellm \
  --model openai/qwen3-coder-next \
  --api_base http://localhost:8000/v1 \
  --drop_params \
  --port 4000 > /tmp/litellm.log 2>&1 &

Requested doc changes

1. Replace pip install litellm with pip install 'litellm[proxy]' in all model-serving guides
2. Add PATH export for Ubuntu: export PATH="$HOME/.local/bin:$PATH"
3. Add a verification step immediately after install:

   litellm --version   # should print version without ImportError

Impact

Trivial fix (docs-only). High user impact due to timing — hits after the longest wait in the entire workflow.