Google Custom Search JSON API deprecation

### Problem

I just saw this on the Google Custom Search JSON API documentation page while trying to set it up for use with the beets lyrics plugin:

> Note: The Custom Search JSON API is closed to new customers. [Vertex AI Search](https://cloud.google.com/use-cases/site-search) is a favorable alternative for searching up to 50 domains. Alternatively, if your use case necessitates full web search, [contact us](https://docs.google.com/forms/d/e/1FAIpQLSfYcIpOzj57MoetWyeFpJf9Cf4yezG5HDq3VsqbJhlngp5pXw/viewform) to express your interest in and get more information about our full web search solution.

> Existing Custom Search JSON API customers have until January 1, 2027 to transition to an alternative solution.

Unfortunately there doesn't appear to be a free tier for Vertex AI Search (if it would even be a good replacement): https://cloud.google.com/use-cases/site-search#pricing

I'm not 100% familiar with the API, so my apologies if this information isn't relevant! I wasn't able to get the lyrics plugin to work with my API key, and I figured this might be the reason.

### Setup

* OS: Linux
* Python version: 3.12.13
* beets version: 2.10.0
* Turning off plugins made problem go away (yes/no): no

Start by reproducing the lyrics plugin failure with Python 3.12.13, beets 2.10.0, and the reported API key setup. Inspect the lyrics plugin's Google Custom Search JSON API usage and confirm whether the failure is caused by the API's customer restrictions; the issue needs a defined supported behavior or replacement before implementation can be considered done.

Written by the indexing model from the issue text.