refactor(profiling): split stack sampler helpers (#18975)

## Description

Pure refactor of existing stack sampler internals, with no intended behavior or internal contract changes, in preparation for timer_create based cpu time profiling in #18724 

Specifically:

- Extracts the existing task/greenlet/thread-stack rendering branch in `ThreadInfo::sample()` into a local `render_unwound_stacks()` helper.
- Extracts duplicate one-time thread registration failure logging in `Sampler::register_thread()` into a local helper.

This does not introduce CPU timer profiling, new configuration, new native bindings, or changes to thread registration semantics.

## Testing

- `scripts/lint cformat`

Attempted a targeted profiling test run from the worktree, but the test runner failed during riot venv setup before executing tests due the worktree using `/home/bits/project/.riot`, which was not writable/available in that context.

## Risks

Low. This is intended to be behavior-preserving refactoring only.

## Additional Notes

No changelog needed, internal refactor only.


Co-authored-by: taegyun.kim <taegyun.kim@datadoghq.com>

Author: taegyunkim

ddtrace/internal/datadog/profiling/stack/echion/echion/threads.h

@@ -111,6 +111,7 @@ class ThreadInfo
     };
 
   private:
+    void render_unwound_stacks(EchionSampler&);
     [[nodiscard]] Result<void> unwind_tasks(EchionSampler&, PyThreadState*);
     void unwind_greenlets(EchionSampler&, PyThreadState*, unsigned long);
     [[nodiscard]] Result<std::vector<TaskInfo::Ptr>> get_all_tasks(EchionSampler&, PyThreadState* tstate);

ddtrace/internal/datadog/profiling/stack/src/echion/threads.cc

@@ -708,21 +708,10 @@ ThreadInfo::unwind_greenlets(EchionSampler& echion, PyThreadState* tstate, unsig
 }
 
 // ----------------------------------------------------------------------------
-Result<void>
-ThreadInfo::sample(EchionSampler& echion, PyThreadState* tstate, microsecond_t delta)
+void
+ThreadInfo::render_unwound_stacks(EchionSampler& echion)
 {
     auto& renderer = echion.renderer();
-    renderer.render_thread_begin(tstate, name, delta, thread_id, native_id);
-
-    microsecond_t previous_cpu_time = cpu_time;
-    auto update_cpu_time_success = update_cpu_time();
-    if (!update_cpu_time_success) {
-        return ErrorKind::CpuTimeError;
-    }
-
-    renderer.render_cpu_time(cpu_time - previous_cpu_time);
-
-    this->unwind(echion, tstate);
 
     // Render in this order of priority
     // 1. asyncio Tasks stacks (if any)
@@ -755,6 +744,25 @@ ThreadInfo::sample(EchionSampler& echion, PyThreadState* tstate, microsecond_t d
         python_stack.render(echion);
         renderer.render_stack_end();
     }
+}
+
+// ----------------------------------------------------------------------------
+Result<void>
+ThreadInfo::sample(EchionSampler& echion, PyThreadState* tstate, microsecond_t delta)
+{
+    auto& renderer = echion.renderer();
+    renderer.render_thread_begin(tstate, name, delta, thread_id, native_id);
+
+    microsecond_t previous_cpu_time = cpu_time;
+    auto update_cpu_time_success = update_cpu_time();
+    if (!update_cpu_time_success) {
+        return ErrorKind::CpuTimeError;
+    }
+
+    renderer.render_cpu_time(cpu_time - previous_cpu_time);
+
+    this->unwind(echion, tstate);
+    this->render_unwound_stacks(echion);
 
     return Result<void>::ok();
 }