Add some performance metrics for Sentry (#5760)

- Add `AnalyticsService.startTransaction(...)` to start a logging transaction that can be uploaded to Sentry if the user enabled the analytics upload.
- Add `AnalyticsTransaction` wrapper to abstract the Sentry ones.
- Added several helper methods to improve the UX around these transactions.
- Then measure:
  - Time until the first sync, and how it ended.
  - Time until the first rooms are displayed.
  - Time to load a room or a preview.
  - Time to load a timeline.

services/analyticsproviders/sentry/src/main/kotlin/io/element/android/services/analyticsproviders/sentry/SentryAnalyticsProvider.kt

@@ -20,6 +20,7 @@ import io.element.android.libraries.core.meta.BuildMeta
 import io.element.android.libraries.core.meta.BuildType
 import io.element.android.libraries.di.annotations.ApplicationContext
 import io.element.android.services.analyticsproviders.api.AnalyticsProvider
+import io.element.android.services.analyticsproviders.api.AnalyticsTransaction
 import io.element.android.services.analyticsproviders.sentry.log.analyticsTag
 import io.sentry.Breadcrumb
 import io.sentry.Sentry
@@ -51,6 +52,7 @@ class SentryAnalyticsProvider(
             options.isEnableUserInteractionTracing = true
             options.environment = buildMeta.buildType.toSentryEnv()
         }
+        Timber.tag(analyticsTag.value).d("Sentry was initialized correctly")
     }
 
     override fun stop() {
@@ -87,6 +89,10 @@ class SentryAnalyticsProvider(
     override fun trackError(throwable: Throwable) {
         Sentry.captureException(throwable)
     }
+
+    override fun startTransaction(name: String, operation: String?): AnalyticsTransaction? {
+        return SentryAnalyticsTransaction(name, operation)
+    }
 }
 
 private fun BuildType.toSentryEnv() = when (this) {

services/analyticsproviders/sentry/src/main/kotlin/io/element/android/services/analyticsproviders/sentry/SentryAnalyticsTransaction.kt

@@ -0,0 +1,24 @@
+/*
+ * Copyright (c) 2025 Element Creations Ltd.
+ *
+ * SPDX-License-Identifier: AGPL-3.0-only OR LicenseRef-Element-Commercial.
+ * Please see LICENSE files in the repository root for full details.
+ */
+
+package io.element.android.services.analyticsproviders.sentry
+
+import io.element.android.services.analyticsproviders.api.AnalyticsTransaction
+import io.sentry.ISpan
+import io.sentry.Sentry
+
+class SentryAnalyticsTransaction private constructor(span: ISpan) : AnalyticsTransaction {
+    constructor(name: String, operation: String?) : this(Sentry.startTransaction(name, operation.orEmpty()))
+    private val inner = span
+
+    override fun startChild(operation: String, description: String?): AnalyticsTransaction = SentryAnalyticsTransaction(
+        inner.startChild(operation, description)
+    )
+    override fun setData(key: String, value: Any) = inner.setData(key, value)
+    override fun isFinished(): Boolean = inner.isFinished
+    override fun finish() = inner.finish()
+}