Move root session ID env lookup to tracer_config.cpp

Read _DD_ROOT_CPP_SESSION_ID in finalize_config() and store it in
FinalizedTracerConfig, consistent with how all other env vars are
handled. Removes the ad-hoc get_root_session_id() helper in tracer.cpp.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Author: khanayan123

include/datadog/tracer_config.h

@@ -225,6 +225,7 @@ class FinalizedTracerConfig final {
   bool log_on_startup;
   bool generate_128bit_trace_ids;
   Optional<RuntimeID> runtime_id;
+  Optional<std::string> root_session_id;
   Clock clock;
   std::string integration_name;
   std::string integration_version;

src/datadog/tracer.cpp

@@ -36,16 +36,6 @@ namespace fs = std::filesystem;
 namespace datadog {
 namespace tracing {
 
-namespace {
-
-std::string get_root_session_id(const std::string& runtime_id) {
-  if (auto val = environment::lookup(environment::_DD_ROOT_CPP_SESSION_ID)) {
-    return std::string(*val);
-  }
-  return runtime_id;
-}
-
-}  // namespace
 
 void to_json(nlohmann::json& j, const PropagationStyle& style) {
   j = to_string_view(style);
@@ -59,7 +49,8 @@ Tracer::Tracer(const FinalizedTracerConfig& config,
     : logger_(config.logger),
       runtime_id_(config.runtime_id ? *config.runtime_id
                                     : RuntimeID::generate()),
-      signature_{runtime_id_, get_root_session_id(runtime_id_.string()),
+      signature_{runtime_id_,
+                 config.root_session_id.value_or(runtime_id_.string()),
                  config.defaults.service, config.defaults.environment},
       config_manager_(std::make_shared<ConfigManager>(config)),
       collector_(/* see constructor body */),

src/datadog/tracer_config.cpp

@@ -407,6 +407,10 @@ Expected<FinalizedTracerConfig> finalize_config(const TracerConfig &user_config,
     final_config.runtime_id = user_config.runtime_id;
   }
 
+  if (auto val = lookup(environment::_DD_ROOT_CPP_SESSION_ID)) {
+    final_config.root_session_id = std::string{*val};
+  }
+
   final_config.process_tags = user_config.process_tags;
 
   auto agent_finalized =