Support Open-source LLM providers alongside Gemini

### What would you like to be added?

Gemini CLI is an excellent terminal AI agent, but it is currently centered around Gemini models. It would be valuable to support a wider range of OpenAI-compatible providers and open-source models through a common provider interface.

This would allow users to choose the model that best fits their needs while keeping the same CLI experience. Examples include self-hosted models, local inference servers, and cloud providers that expose OpenAI-compatible APIs.

I've been experimenting with this idea in my own project, Open Agent, which adapts the Gemini CLI experience to work with 100+ models, local LLMs, Docker sandboxing, and multiple providers. Some of the implementation ideas there may be useful if broader model support is ever considered:

https://github.com/haseeb-heaven/open-agent

### Why is this needed?

Many developers already use open-source models for privacy, offline development, lower cost, or provider flexibility.

Adding support for multiple providers would:

Reduce vendor lock-in.
Enable local and self-hosted models.
Allow users to choose between Gemini and open-source models.
Make the CLI useful in environments where Gemini is unavailable.
Encourage community contributions around new providers.

Gemini would still remain a first-class option, while users who prefer other models could use the same workflow.

### Additional context

Open Agent demonstrates one possible approach by keeping the familiar Gemini CLI workflow while adding support for:

100+ AI models
OpenAI-compatible providers
Local LLMs
Docker sandbox execution
Provider-agnostic configuration

This isn't intended as a replacement for Gemini CLI, but as an example that broader provider support is both feasible and useful.

No files or tests are named in the issue. Start by reviewing Gemini CLI’s existing provider and model configuration, then compare the Open Agent reference linked in the issue. Done means the CLI supports selectable Gemini, OpenAI-compatible, local, and self-hosted providers through a common workflow.

Written by the indexing model from the issue text.