azure-ai-inference needs typing updates for pyright version 1.1.405

**ACTION NEEDED:** This version of pyright will be merged on **2026-01-12**. The build will begin to fail for this library if errors are not fixed.

**Library name:** azure-ai-inference
**Pyright version:** 1.1.405
**Pyright Build:** [Link to build (2025-11-08)](https://dev.azure.com/azure-sdk/internal/_build/results?buildId=5550801&view=logs&j=e5b925a9-9650-5321-24fd-5d9499fe02b8&t=d243185e-b901-5eef-29fe-f7943e030451)
**How to fix:** Run the `next-pyright` tox command at the library package-level and resolve the typing errors.
1) `../azure-ai-inference>pip install "tox<5"`
2) `../azure-ai-inference>tox run -e next-pyright -c ../../../eng/tox/tox.ini --root .`

See the [Typing Guide](https://github.com/Azure/azure-sdk-for-python/blob/main/doc/dev/static_type_checking.md#run-mypy) for more information.