[cq] Migrate startup initializers to use the `ProjectActivity` API

[pq]

The current approach is deprecated, unstable and subject to removal.

Specifically, we need to update:

• FlutterInitializer and
• FlutterStudioStartupActivity

(See stacktrace below.)

2025-04-23 08:23:25,396 [  81501]   WARN - #c.i.i.s.i.StartupManagerImpl - Migrate io.flutter.FlutterInitializer to ProjectActivity [Plugin: io.flutter]
com.intellij.diagnostic.PluginException: Migrate io.flutter.FlutterInitializer to ProjectActivity [Plugin: io.flutter]
	at com.intellij.ide.startup.impl.StartupManagerImpl.doRunPostStartupActivities(StartupManagerImpl.kt:293)
	at com.intellij.ide.startup.impl.StartupManagerImpl.access$doRunPostStartupActivities(StartupManagerImpl.kt:70)
	at com.intellij.ide.startup.impl.StartupManagerImpl$runPostStartupActivities$3$2.invokeSuspend(StartupManagerImpl.kt:196)
	at com.intellij.ide.startup.impl.StartupManagerImpl$runPostStartupActivities$3$2.invoke(StartupManagerImpl.kt)
	at com.intellij.ide.startup.impl.StartupManagerImpl$runPostStartupActivities$3$2.invoke(StartupManagerImpl.kt)
	at kotlinx.coroutines.intrinsics.UndispatchedKt.startUndispatchedOrReturn(Undispatched.kt:62)
	at kotlinx.coroutines.BuildersKt__Builders_commonKt.withContext(Builders.common.kt:163)
	at kotlinx.coroutines.BuildersKt.withContext(Unknown Source)
	at com.intellij.ide.startup.impl.StartupManagerImpl$runPostStartupActivities$3.invokeSuspend(StartupManagerImpl.kt:195)
	at kotlin.coroutines.jvm.internal.BaseContinuationImpl.resumeWith(ContinuationImpl.kt:33)
	at kotlinx.coroutines.DispatchedTask.run(DispatchedTask.kt:104)
	at kotlinx.coroutines.scheduling.CoroutineScheduler.runSafely(CoroutineScheduler.kt:608)
	at kotlinx.coroutines.scheduling.CoroutineScheduler$Worker.executeTask(CoroutineScheduler.kt:873)
	at kotlinx.coroutines.scheduling.CoroutineScheduler$Worker.runWorker(CoroutineScheduler.kt:763)
	at kotlinx.coroutines.scheduling.CoroutineScheduler$Worker.run(CoroutineScheduler.kt:750)
2025-04-23 08:23:25,398 [  81503]   WARN - #c.i.i.s.i.StartupManagerImpl - Migrate io.flutter.FlutterStudioStartupActivity to ProjectActivity [Plugin: io.flutter]
com.intellij.diagnostic.PluginException: Migrate io.flutter.FlutterStudioStartupActivity to ProjectActivity [Plugin: io.flutter]
	at com.intellij.ide.startup.impl.StartupManagerImpl.doRunPostStartupActivities(StartupManagerImpl.kt:293)
	at com.intellij.ide.startup.impl.StartupManagerImpl.access$doRunPostStartupActivities(StartupManagerImpl.kt:70)
	at com.intellij.ide.startup.impl.StartupManagerImpl$runPostStartupActivities$3$2.invokeSuspend(StartupManagerImpl.kt:196)
	at com.intellij.ide.startup.impl.StartupManagerImpl$runPostStartupActivities$3$2.invoke(StartupManagerImpl.kt)
	at com.intellij.ide.startup.impl.StartupManagerImpl$runPostStartupActivities$3$2.invoke(StartupManagerImpl.kt)
	at kotlinx.coroutines.intrinsics.UndispatchedKt.startUndispatchedOrReturn(Undispatched.kt:62)
	at kotlinx.coroutines.BuildersKt__Builders_commonKt.withContext(Builders.common.kt:163)
	at kotlinx.coroutines.BuildersKt.withContext(Unknown Source)

See also: #7718