chore(opentelemetry-instrumentation): improve _warnOnPreloadedModules function not to show warning logs when the module is not marked as loaded

Author: rlj1202

CHANGELOG.md

@@ -14,6 +14,8 @@ For notes on migrating to 2.x / 0.200.x see [the upgrade guide](doc/upgrade-to-2
 
 ### :rocket: Features
 
+* chore(opentelemetry-instrumentation): improve `_warnOnPreloadedModules` function not to show warning logs when the module is not marked as loaded [#6095](https://github.com/open-telemetry/opentelemetry-js/pull/6095) @rlj1202
+
 ### :bug: Bug Fixes
 
 ### :books: Documentation

experimental/packages/opentelemetry-instrumentation/src/platform/node/instrumentation.ts

@@ -148,7 +148,7 @@ export abstract class InstrumentationBase<
       const { name } = module;
       try {
         const resolvedModule = require.resolve(name);
-        if (require.cache[resolvedModule]) {
+        if (require.cache[resolvedModule]?.loaded) {
           // Module is already cached, which means the instrumentation hook might not work
           this._diag.warn(
             `Module ${name} has been loaded before ${this.instrumentationName} so it might not work, please initialize it before requiring ${name}`