feat: Support proxying instrumentation telemetry API payloads (#777)

## Ticket
https://datadoghq.atlassian.net/browse/SVLS-7324

## Overview
Instrumentation Telemetry is not enabled for Lambda. This PR adds
support for it.

## Testing
Deployed for testing and checked logs:
`DD_EXTENSION | DEBUG | Trace Agent | Proxied request for
instrumentation`
`DD_EXTENSION | DEBUG | Proxy Flusher | Successfully sent request in 340
ms to
https://instrumentation-telemetry-intake.datadoghq.com/api/v2/apmtelemetry`

Author: jchrostek-dd

bottlecap/src/traces/trace_agent.rs

@@ -53,6 +53,7 @@ const LLM_OBS_EVAL_METRIC_ENDPOINT_PATH_V2: &str =
 const LLM_OBS_SPANS_ENDPOINT_PATH: &str = "/evp_proxy/v2/api/v2/llmobs";
 const INFO_ENDPOINT_PATH: &str = "/info";
 const DEBUGGER_ENDPOINT_PATH: &str = "/debugger/v1/input";
+const INSTRUMENTATION_ENDPOINT_PATH: &str = "/telemetry/proxy/api/v2/apmtelemetry";
 
 // Intake endpoints
 const DSM_INTAKE_PATH: &str = "/api/v0.1/pipeline_stats";
@@ -61,6 +62,7 @@ const LLM_OBS_EVAL_METRIC_INTAKE_PATH: &str = "/api/intake/llm-obs/v1/eval-metri
 const LLM_OBS_EVAL_METRIC_INTAKE_PATH_V2: &str = "/api/intake/llm-obs/v2/eval-metric";
 const PROFILING_INTAKE_PATH: &str = "/api/v2/profile";
 const DEBUGGER_LOGS_INTAKE_PATH: &str = "/api/v2/logs";
+const INSTRUMENTATION_INTAKE_PATH: &str = "/api/v2/apmtelemetry";
 
 const TRACER_PAYLOAD_CHANNEL_BUFFER_SIZE: usize = 10;
 const STATS_PAYLOAD_CHANNEL_BUFFER_SIZE: usize = 10;
@@ -231,6 +233,10 @@ impl TraceAgent {
             )
             .route(LLM_OBS_SPANS_ENDPOINT_PATH, post(Self::llm_obs_spans_proxy))
             .route(DEBUGGER_ENDPOINT_PATH, post(Self::debugger_logs_proxy))
+            .route(
+                INSTRUMENTATION_ENDPOINT_PATH,
+                post(Self::instrumentation_proxy),
+            )
             .with_state(proxy_state);
 
         let info_router = Router::new().route(INFO_ENDPOINT_PATH, any(Self::info));
@@ -366,6 +372,18 @@ impl TraceAgent {
         .await
     }
 
+    async fn instrumentation_proxy(State(state): State<ProxyState>, request: Request) -> Response {
+        Self::handle_proxy(
+            state.config,
+            state.proxy_aggregator,
+            request,
+            "instrumentation-telemetry-intake",
+            INSTRUMENTATION_INTAKE_PATH,
+            "instrumentation",
+        )
+        .await
+    }
+
     #[allow(clippy::unused_async)]
     async fn info() -> Response {
         let response_json = json!(