Bring over embeddings support from the PHP AI Client - #892

What?

Brings the embedding related changes over from the PHP AI Client and loads those conditionally when needed, allowing us to start supporting that work.

Why?

Embedding supported was added to v1.4.0 of the PHP AI Client. We were hoping to get this in to WordPress 7.1 but that has been pushed now to 7.2. Instead of having to wait until WordPress 7.2 is released to take advantage of this new functionality, this PR pulls that code into the AI plugin, behind a conditional gate, so we can start taking advantage of that earlier.

How?

• Pulls the embedding related code from the PHP AI Client into an includes/Vendor/AiClient directory
• Adds an SDK_Overlay class that loads this code, if needed, on top of the code WordPress itself loads. This allows us to continue to use the PHP AI Client that ships with WordPress while also loading in this new embedding code. This approach can be used in the future for any other PHP AI Client changes we want to start using sooner
• Adds in helper functions that can be used to determine if embedding generation is supported via the PHP AI Client and can be used to generate embeddings

Use of AI Tools

AI assistance: Yes
Tool(s): Claude Code
Model(s): Opus 4.8
Used for: Brainstorming and planning the initial approach and then executing on that approach. Final review and testing by me

Testing Instructions

Easiest way to test is via the custom WP-CLI command this PR has. Note you'll also need to install an AI Provider plugin that supports embeddings.

1. Pull this PR down
2. Ensure you have an AI Provider plugin installed, activated and configured that supports embeddings: OpenAI PR, Google PR, Ollama PR
3. Open up a terminal window
4. Run wp ai embeddings generate 'This is some text'
5. You should get a message like Dry run: would have generated embeddings for text: This is some text
6. Run wp ai embeddings generate 'This is some text' --dry-run=false
7. You should see a success message and information about the provider and model used as well as the embedding value (trimmed)
8. Try other versions of the command and ensure they work as expected:

• wp ai embeddings generate --post-id=42 --dry-run=false
• wp ai embeddings generate --post-id=42 --chunk --dry-run=false
• wp ai embeddings generate 'This is some text' --provider=ollama --dry-run=false

Changelog Entry

Added - Brought the embedding code over from the PHP AI Client and load that conditionally so those using the AI plugin can start to take advantage of embedding generation.