Drops the serde_eventsource dependency

serde_eventsource is taking a while to update to reqwest 13.*. This
PR implements handling SSE in the library code.

examples/raw_sse.rs

@@ -0,0 +1,37 @@
+use std::env;
+
+use google_genai::{
+    network::event_source::EventSource,
+    prelude::{Content, GenerateContentRequest, Role},
+};
+use tokio_stream::StreamExt;
+
+static MODEL: &str = "gemini-2.5-flash";
+
+#[tokio::main]
+pub async fn main() {
+    let prompt = vec![
+        Content::builder()
+            .role(Role::User)
+            .add_text_part("What is the airspeed of an unladen swallow?")
+            .build(),
+    ];
+    let request = GenerateContentRequest::builder().contents(prompt).build();
+    let _ = dotenvy::dotenv();
+    let api_key = env::var("GEMINI_API_KEY").unwrap();
+    let client = reqwest::Client::new();
+    let endpoint_url = format!(
+        "https://generativelanguage.googleapis.com/v1beta/models/{MODEL}:streamGenerateContent?alt=sse"
+    );
+    let mut event_stream = client
+        .post(&endpoint_url)
+        .header("x-goog-api-key", api_key)
+        .json(&request)
+        .send()
+        .await
+        .unwrap()
+        .event_stream();
+    while let Some(event) = event_stream.next().await {
+        println!("{event:?}")
+    }
+}