Fix AzureAI Search issues

[MikeAlhayek]

In this PR I fix the following issues that I encountered with Azure AI

1. The Search Index content Part and Type settings was not saving the Included flag.
2. Ensure we save IndexName and IndexFullName to the settings document.
3. Fix AzureAISearchIndexSettings recipe step

[Piedone]

Why don't merge?

[MikeAlhayek]

@Piedone because I thought of something else and did not want someone to merge it yet. Anyway, it's ready not. If you like you can review it.

[Piedone]

In that case, you can convert it into a draft, that communicates the in-progress intent quite well.

I don't really know anything about AI search, so I'm probably not the best person to review this.

[MikeAlhayek]

Yeah I think I am the only one that is using it :)