Remove BROWSERBASE_PROJECT_ID requirement (#625)

* Remove BROWSERBASE_PROJECT_ID requirement

The Browserbase API no longer requires a project ID to create sessions —
it is inferred from the API key. Remove the env var requirement from both
the TypeScript daemon and Rust CLI, and update docs accordingly.

* Remove unnecessary Content-Type header since no body is sent

cli/src/native/providers.rs

@@ -82,15 +82,11 @@ pub async fn close_provider_session(session: &ProviderSession) {
 async fn connect_browserbase() -> Result<(String, Option<ProviderSession>), String> {
     let api_key = env::var("BROWSERBASE_API_KEY")
         .map_err(|_| "BROWSERBASE_API_KEY environment variable is not set")?;
-    let project_id = env::var("BROWSERBASE_PROJECT_ID")
-        .map_err(|_| "BROWSERBASE_PROJECT_ID environment variable is not set")?;
 
     let client = reqwest::Client::new();
     let response = client
         .post("https://api.browserbase.com/v1/sessions")
-        .header("Content-Type", "application/json")
         .header("X-BB-API-Key", &api_key)
-        .json(&json!({ "projectId": project_id }))
         .send()
         .await
         .map_err(|e| format!("Browserbase request failed: {}", e))?;