[XrossFox]

Description

Remove deprecated BigQuery Connection snippets (DeleteConnection, GetConnection, ListConnections, and UpdateConnection) and their corresponding integration tests, as they have been superseded by samples in googleapis/google-cloud-java.

Inline connection cleanup in the remaining integration tests' tearDown() methods so they no longer depend on DeleteConnection.

Fixes b/576442220

Checklist

Testing

• I have tested this change on a live environment and verified it works as intended.
• Tests pass: mvn clean verify required
• Lint passes: mvn -P lint checkstyle:check required
• Static Analysis: mvn -P lint clean compile pmd:cpd-check spotbugs:check advisory only

Compliance & Style

• I have followed Sample Format Guide
• pom.xml parent set to latest shared-configuration
• Appropriate changes to README are included in PR
• This sample adds a new sample directory, and I updated the CODEOWNERS file with the codeowners for this sample
• This sample adds a new Product API, and I updated the Blunderbuss issue/PR auto-assigner with the codeowners for this sample

Post-Approval Actions

• Please merge this PR for me once it is approved

[snippet-bot]

Here is the summary of changes.

You are about to delete 4 region tags.

• bigquery/bigqueryconnection/snippets/src/main/java/com/example/bigqueryconnection/DeleteConnection.java:19, tag bigqueryconnection_delete_connection
• bigquery/bigqueryconnection/snippets/src/main/java/com/example/bigqueryconnection/GetConnection.java:19, tag bigqueryconnection_get_connection
• bigquery/bigqueryconnection/snippets/src/main/java/com/example/bigqueryconnection/ListConnections.java:19, tag bigqueryconnection_list_connections
• bigquery/bigqueryconnection/snippets/src/main/java/com/example/bigqueryconnection/UpdateConnection.java:19, tag bigqueryconnection_update_connection

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[gemini-code-assist]

Code Review

This pull request removes several standalone connection classes (DeleteConnection, GetConnection, ListConnections, UpdateConnection) along with their integration tests. The remaining integration tests (CreateAwsConnectionIT, CreateConnectionIT, and ShareConnectionIT) are updated to perform connection cleanup directly in their tearDown methods. The review feedback highlights a potential issue where an exception during cleanup could prevent the restoration of the standard output stream, and suggests wrapping the cleanup logic in a try-finally block to ensure the stream is always restored.