[ai] Migrate ai projects to use snippets extraction

[mpodwysocki]

Packages impacted by this PR

• @azure/ai-projects

Issues associated with this PR

• [snippets] Add README snippets for all projects #32416

Describe the problem that is addressed by this PR

Updates all projects under ai to use snippets extraction.

What are the possible designs available to address the problem? If there are more than one possible design, why was the one in this PR chosen?

Are there test cases added in this PR? (If not, why?)

Provide a list of related PRs (if any)

Command used to generate this PR:**(Applicable only to SDK release request PRs)

Checklists

• Added impacted package name to the issue description
• Does this PR needs any fixes in the SDK Generator?** (If so, create an Issue in the Autorest/typescript repository and link it here)
• Added a changelog (if necessary)

[azure-sdk]

API change check

API changes are not detected in this pull request.

[ganeshyb]

@GraceBrigham you have made similar changes as part of this PR #32508
@ZachhK this would introduce conflicts with your PR for beta 3

[GraceBrigham]

@GraceBrigham you have made similar changes as part of this PR #32508 @ZachhK this would introduce conflicts with your PR for beta 3

It looks like those changes got reverted somewhere as they aren't in main.

[mpodwysocki]

@GraceBrigham you have made similar changes as part of this PR #32508 @ZachhK this would introduce conflicts with your PR for beta 3

@ganeshyb I can make any updates on this PR for Beta 3 if you would like, but as is, it is pretty complete right now. Feel free to close this PR if this conflicts with your Beta 3 plans.