ReaderRevenueSubscriptionLinking: Unexpected POST Request Instead of PATCH When Calling `UpdateEntitlements`

When instantiating `SubscribewithGoogle` using `com.google.api.client.http.javanet.NetHttpTransport`, and calling the `UpdateEntitlements` method from the Reader Revenue Subscription Linking API (v1), a **POST** request is sent instead of the expected **PATCH** request.

Reference:
UpdateEntitlements method source
https://github.com/googleapis/google-api-java-client-services/blob/700b41fb705bb8b817f5d4103ccfed5f411866e6/clients/google-api-services-readerrevenuesubscriptionlinking/v1/2.0.0/com/google/api/services/readerrevenuesubscriptionlinking/v1/SubscriptionLinking.java#L649

#### Environment details

1. OS Type and Version
Windows 11 (64-bit)

2. Java Version
`1.8.0_60`
Java(TM) SE Runtime Environment (build 1.8.0_60-b27)
Java HotSpot(TM) Client VM (build 25.60-b23, mixed mode)

3. Library Versions
```gradle
implementation 'com.google.api-client:google-api-client:2.6.0'
implementation 'com.google.auth:google-auth-library-oauth2-http:1.23.0'
implementation 'com.google.apis:google-api-services-androidpublisher:v3-rev20240709-2.0.0'
implementation 'com.google.apis:google-api-services-readerrevenuesubscriptionlinking:v1-rev20250611-2.0.0'
implementation 'org.apache.httpcomponents:httpclient:4.5.13'
```

4. Build Tools
- Gradle 7.0.2
- Apache Ant(TM) version 1.10.9
- JVM: 1.8.0_60 (Oracle Corporation 25.60-b23)

#### Steps to reproduce

1. Instantiate `SubscribewithGoogle` using `com.google.api.client.http.javanet.NetHttpTransport`.
2. Call the `UpdateEntitlements` method from the Reader Revenue Subscription Linking API v1.

#### Any additional information below
Additionally, although deprecated, we confirmed that using an instance of `com.google.api.client.http.apache.ApacheHttpTransport` results in a **PATCH** request being sent as expected.