feat: Add LiteLLM provider with automatic prompt caching support (#3380)

Signed-off-by: HikaruEgashira <account@egahika.dev>

crates/goose/src/providers/factory.rs

@@ -12,6 +12,7 @@ use super::{
     google::GoogleProvider,
     groq::GroqProvider,
     lead_worker::LeadWorkerProvider,
+    litellm::LiteLLMProvider,
     ollama::OllamaProvider,
     openai::OpenAiProvider,
     openrouter::OpenRouterProvider,
@@ -50,6 +51,7 @@ pub fn providers() -> Vec<ProviderMetadata> {
         // GithubCopilotProvider::metadata(),
         GoogleProvider::metadata(),
         GroqProvider::metadata(),
+        LiteLLMProvider::metadata(),
         OllamaProvider::metadata(),
         OpenAiProvider::metadata(),
         OpenRouterProvider::metadata(),
@@ -158,6 +160,7 @@ fn create_provider(name: &str, model: ModelConfig) -> Result<Arc<dyn Provider>>
         "databricks" => Ok(Arc::new(DatabricksProvider::from_env(model)?)),
         "gemini-cli" => Ok(Arc::new(GeminiCliProvider::from_env(model)?)),
         "groq" => Ok(Arc::new(GroqProvider::from_env(model)?)),
+        "litellm" => Ok(Arc::new(LiteLLMProvider::from_env(model)?)),
         "ollama" => Ok(Arc::new(OllamaProvider::from_env(model)?)),
         "openrouter" => Ok(Arc::new(OpenRouterProvider::from_env(model)?)),
         "gcp_vertex_ai" => Ok(Arc::new(GcpVertexAIProvider::from_env(model)?)),