Iteration 2: Duo Chat: simplify the chunks handling after delegating this work to UI component

This is the next step after Iteration 1: Move chunks handling back to the U... (gitlab-ui#2579 - closed) to remove the maintenance burden from Duo Chat consumers.

Iteration 1: Move chunks handling back to the U... (gitlab-ui#2579 - closed) re-introduces the logic of handling the chunks when streaming to the shared UI component in a backwards-compatible manner. This issue is meant as a clean-up for the VSCode extension to remove special handling of the chunks and mutation of the message object. The places that might need to be updated (the list might be not extensive):

• https://gitlab.com/gitlab-org/gitlab-vscode-extension/-/blob/main/src/common/chat/gitlab_chat_record.ts#L76
• https://gitlab.com/gitlab-org/gitlab-vscode-extension/-/blob/main/src/common/chat/gitlab_chat_api.ts#L181