[Backport 8.x] [Inference API] Adds chunking_settings to PUT inference API

[github-actions]

Backport bf2a5ca from #3781.

[github-actions]

Following you can find the validation results for the APIs you have changed.

API	Status	Request	Response
inference.delete	⚪	Missing test	Missing test
inference.get	🟢	1/1	1/1
inference.inference	⚪	Missing test	Missing test
inference.put	⚪	Missing test	Missing test
inference.stream_inference	⚪	Missing test	Missing test
inference.unified_inference	⚪	Missing test	Missing test
inference.update	⚪	Missing test	Missing test

You can validate these APIs yourself by using the make validate target.