[operator] Cannot customize TheiaCloudClient due to overriding restrictions in Guice

### Describe the bug

Follow-up of https://github.com/eclipse-theia/theia-cloud/issues/433 that has been closed without any resolution.

From https://github.com/eclipse-theia/theia-cloud/issues/433#issue-3188840367:

> ### Describe the bug
> The current design of `AbstractTheiaCloudOperatorModule` in Theia Cloud does not support customization of certain dependencies, particularly when attempting to override `@Provides` methods using `Modules.override`.
>
> Our use case:
>
> When we enable the `activity-tracker`, additional logic in `TheiaCloudClient` (such as calls to `getClusterIPFromSessionName`) is triggered. To inspect (errors like `No ClusterIP found for session`) and enhance this behavior, we subclass `TheiaCloudClient` and want to inject our custom version.
>
> However, the framework defines a `@Provides` method like the following:
>
> @Provides
> @Singleton
> protected TheiaCloudClient provideTheiaCloudClient(NamespacedKubernetesClient client) {
> return new DefaultTheiaCloudClient(client);
> }
> #### Problem 1: Overriding the provider method directly causes a runtime error
> @Override
> protected TheiaCloudClient provideTheiaCloudClient(NamespacedKubernetesClient client) {
> return new MyTheiaCloudClient(client);
> }
> Results in:
>
> ```
> Overriding @Provides methods is not allowed.
> @Provides method: AbstractTheiaCloudOperatorModule.provideTheiaCloudClient()
> overridden by: MyOperatorModule.provideTheiaCloudClient()
> ```
>
> #### Problem 2: Defining a second provider method causes a binding conflict
> @Provides
> @Singleton
> protected TheiaCloudClient provideCustomTheiaCloudClient(NamespacedKubernetesClient client) {
> return new MyTheiaCloudClient(client);
> }
> Produces:
>
> ```
> [Guice/BindingAlreadySet]: TheiaCloudClient was bound multiple times.
> Bound at:
> 1 : MyMonitorMessagingServiceTest$1.configure(MyMonitorMessagingServiceTest.java:91)
> \_ installed by: Modules$OverrideModule -> MyMonitorMessagingServiceTest$1
> 2 : AbstractTheiaCloudOperatorModule.provideTheiaCloudClient(AbstractTheiaCloudOperatorModule.java:165)
> \_ installed by: Modules$OverrideModule -> MyOperatorModule
> ```
>
> #### Problem 3: `Modules.override(...)` cannot return an `AbstractTheiaCloudOperatorModule` type
> Attempting to override with:
>
> @Override
> public AbstractTheiaCloudOperatorModule createModule(TheiaCloudOperatorArguments arguments) {
> return Modules.override(new MyOperatorModule(arguments)).with(new AbstractModule() {
> @Override
> protected void configure() {
> // attempt to customize the provider
> }
> });
> }
> ...fails at compile time because `Modules.override(...)` returns only a `Module`, not an `AbstractTheiaCloudOperatorModule`.
>
> This restriction exists even though [the launcher does not use the specific API of `AbstractTheiaCloudOperatorModule`](https://github.com/eclipse-theia/theia-cloud/blob/55813e2c212b0b787fa4181affe466f987f0337a/java/operator/org.eclipse.theia.cloud.operator/src/main/java/org/eclipse/theia/cloud/operator/LeaderElectionTheiaCloudOperatorLauncher.java#L108-L117). The type is only passed to Guice as a module:
>
> protected void startOperatorAsLeader(TheiaCloudOperatorArguments arguments) {
> AbstractTheiaCloudOperatorModule module = this.createModule(arguments);
> Injector injector = Guice.createInjector(module);
> TheiaCloudOperator theiaCloud = injector.getInstance(TheiaCloudOperator.class);
> theiaCloud.start();
> }
> Maybe I am doing something wrong. What is the correct way of customizing the default Theia Cloud client? Thank you!
>
> ### Expected behavior
> The framework provides a way to customize the operator.
>
> ### Cluster provider
> _No response_
>
> ### Version
> _No response_
>
> ### Additional information
> Related [#426 (comment)](https://github.com/eclipse-theia/theia-cloud/issues/426#issue-3060187598)
>
> I am new to this API, but I do not understand why getting the IP requires a new client creation when it is already set at the constructor of the default implementation:
>
> [theia-cloud/java/common/org.eclipse.theia.cloud.common/src/main/java/org/eclipse/theia/cloud/common/k8s/client/TheiaCloudClient.java](https://github.com/eclipse-theia/theia-cloud/blob/55813e2c212b0b787fa4181affe466f987f0337a/java/common/org.eclipse.theia.cloud.common/src/main/java/org/eclipse/theia/cloud/common/k8s/client/TheiaCloudClient.java#L81)
>
> Line 81 in [55813e2](/eclipse-theia/theia-cloud/commit/55813e2c212b0b787fa4181affe466f987f0337a)
>
> try (final KubernetesClient client = new KubernetesClientBuilder().build()) {
> [theia-cloud/java/common/org.eclipse.theia.cloud.common/src/main/java/org/eclipse/theia/cloud/common/k8s/client/DefaultTheiaCloudClient.java](https://github.com/eclipse-theia/theia-cloud/blob/55813e2c212b0b787fa4181affe466f987f0337a/java/common/org.eclipse.theia.cloud.common/src/main/java/org/eclipse/theia/cloud/common/k8s/client/DefaultTheiaCloudClient.java#L28-L31)
>
> Lines 28 to 31 in [55813e2](/eclipse-theia/theia-cloud/commit/55813e2c212b0b787fa4181affe466f987f0337a)
>
> public DefaultTheiaCloudClient(Client client) {
> super(client.adapt(KubernetesClientImpl.class));
> this.client = client.adapt(NamespacedKubernetesClient.class);
> }

### Expected behavior

The framework provides a way to customize the operator.

### Cluster provider

_No response_

### Version

_No response_

### Additional information

_No response_

Start with AbstractTheiaCloudOperatorModule and LeaderElectionTheiaCloudOperatorLauncher, then inspect TheiaCloudClient and DefaultTheiaCloudClient for the existing provider and construction path. Determine how a custom TheiaCloudClient can be bound without Guice override conflicts or the module type restriction. Done means the framework documents or supports a working customization path for the operator.

Written by the indexing model from the issue text.