fix: O11Y-725 - Bug fix to avoid creating multiple OpenTelemetryRum instances when secondaryMobileKeys are set (#281)

## Summary
- This will probably be rewritten as part of
[O11Y-726](https://launchdarkly.atlassian.net/browse/O11Y-726)

[O11Y-726]:
https://launchdarkly.atlassian.net/browse/O11Y-726?atlOrigin=eyJpIjoiNWRkNTljNzYxNjVmNDY3MDlhMDU5Y2ZhYzA5YTRkZjUiLCJwIjoiZ2l0aHViLWNvbS1KU1cifQ

<!-- CURSOR_SUMMARY -->
---

> [!NOTE]
> Gate Observability initialization to the primary mobile key and update
the app to pass it, avoiding multiple OTel instances with secondary
keys.
> 
> - **SDK Plugin (`Observability.kt`)**:
> - Add `mobileKey` constructor parameter and use it to gate
`register(...)` so the observability client/resources initialize only
when `metadata.credential` matches the primary `mobileKey`.
> - Initialization of `Resource` attributes and `ObservabilityClient`
now occurs only under this condition.
> - **E2E App (`BaseApplication.kt`)**:
> - Update `Observability` instantiation to pass `mobileKey =
LAUNCHDARKLY_MOBILE_KEY`.
> 
> <sup>Written by [Cursor
Bugbot](https://cursor.com/dashboard?tab=bugbot) for commit
7974321. This will update automatically
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[here](https://cursor.com/dashboard?tab=bugbot).</sup>
<!-- /CURSOR_SUMMARY -->

Author: agrognetti

e2e/android/app/src/main/java/com/example/androidobservability/BaseApplication.kt

@@ -48,6 +48,7 @@ open class BaseApplication : Application() {
     open fun realInit() {
         val observabilityPlugin = Observability(
             application = this@BaseApplication,
+            mobileKey = LAUNCHDARKLY_MOBILE_KEY,
             options = testUrl?.let { pluginOptions.copy(backendUrl = it, otlpEndpoint = it) } ?: pluginOptions
         )
 

sdk/@launchdarkly/observability-android/lib/src/main/kotlin/com/launchdarkly/observability/plugin/Observability.kt

@@ -32,9 +32,9 @@ import java.util.Collections
  *     )
  *     .build()
  * ```
- * 
+ *
  * Later after initialization you can use [LDObserve] to record observability data.
- * 
+ *
  * ```
  * LDObserve.recordMetric(metric)
  * LDObserve.recordLog(message, severity, attributes)
@@ -44,9 +44,11 @@ import java.util.Collections
  *
  * @param application The application instance.
  * @param options The options for the plugin.
+ * @param mobileKey The primary mobile key used in LDConfig.
  */
 class Observability(
     private val application: Application,
+    private val mobileKey: String,
     private val options: Options = Options() // new instance has reasonable defaults
 ) : Plugin() {
     private val logger: LDLogger
@@ -69,28 +71,30 @@ class Observability(
     override fun register(client: LDClient, metadata: EnvironmentMetadata?) {
         val sdkKey = metadata?.credential ?: ""
 
-        val resourceBuilder = Resource.getDefault().toBuilder()
-        resourceBuilder.put("service.name", options.serviceName)
-        resourceBuilder.put("service.version", options.serviceVersion)
-        resourceBuilder.put("highlight.project_id", sdkKey)
-        resourceBuilder.putAll(options.resourceAttributes)
+        if (mobileKey == sdkKey) {
+            val resourceBuilder = Resource.getDefault().toBuilder()
+            resourceBuilder.put("service.name", options.serviceName)
+            resourceBuilder.put("service.version", options.serviceVersion)
+            resourceBuilder.put("highlight.project_id", sdkKey)
+            resourceBuilder.putAll(options.resourceAttributes)
 
-        metadata?.applicationInfo?.applicationId?.let {
-            resourceBuilder.put("launchdarkly.application.id", it)
-        }
+            metadata?.applicationInfo?.applicationId?.let {
+                resourceBuilder.put("launchdarkly.application.id", it)
+            }
 
-        metadata?.applicationInfo?.applicationVersion?.let {
-            resourceBuilder.put("launchdarkly.application.version", it)
-        }
+            metadata?.applicationInfo?.applicationVersion?.let {
+                resourceBuilder.put("launchdarkly.application.version", it)
+            }
 
-        metadata?.sdkMetadata?.name?.let { sdkName ->
-            metadata.sdkMetadata?.version?.let { sdkVersion ->
-                resourceBuilder.put("launchdarkly.sdk.version", "$sdkName/$sdkVersion")
+            metadata?.sdkMetadata?.name?.let { sdkName ->
+                metadata.sdkMetadata?.version?.let { sdkVersion ->
+                    resourceBuilder.put("launchdarkly.sdk.version", "$sdkName/$sdkVersion")
+                }
             }
-        }
 
-        observabilityClient = ObservabilityClient(application, sdkKey, resourceBuilder.build(), logger, options)
-        observabilityClient?.let { LDObserve.init(it) }
+            observabilityClient = ObservabilityClient(application, sdkKey, resourceBuilder.build(), logger, options)
+            observabilityClient?.let { LDObserve.init(it) }
+        }
     }
 
     override fun getHooks(metadata: EnvironmentMetadata?): MutableList<Hook> {