The sink is MySQL. After running in STREAMING mode for a period of time, it throws the error "No operations allowed after statement closed". How can I resolve this issue?

### Search before asking

- [x] I had searched in the [issues](https://github.com/apache/seatunnel/issues?q=is%3Aissue+label%3A%22bug%22) and found no similar issues.

### What happened

In MySQL‑CDC mode with MySQL as the sink in STREAMING mode, this error occurs after running for a period of time. It is presumed that the connection becomes invalid, yet Seatunnel still tries to use this connection without mechanisms such as connection liveness detection.

### SeaTunnel Version

2.3.12

### SeaTunnel Config

```conf
sink {
jdbc {
url = "jdbc:mysql://localhost:3306/a?useSSL=false&serverTimezone=Asia/Shanghai"
driver = "com.mysql.cj.jdbc.Driver"
user = "xx"
password = "xx"
max_retries = 5

table = "${table_name}"
generate_sink_sql = true

connection_check_timeout_sec = 1800
properties {
connection-test-query = "select 1"
validation-timeout = 3000
max-lifetime = 600000
leak-detection-threshold = 60000
}

database = a

primary_keys = ["${primary_key}"]


}
}
```

### Running Command

```shell
./seatunnel.sh --config ../config/a.conf
```

### Error Exception

```log
Caused by: java.sql.SQLException:No operations allowed after statement closed
```

### Zeta or Flink or Spark Version

_No response_

### Java or Scala Version

_No response_

### Screenshots

_No response_

### Are you willing to submit PR?

- [ ] Yes I am willing to submit a PR!

### Code of Conduct

- [x] I agree to follow this project's [Code of Conduct](https://www.apache.org/foundation/policies/conduct)

No source file or test is named in the report. Start by reproducing the MySQL-CDC to MySQL streaming job with the supplied JDBC sink configuration and inspect how connection_check_timeout_sec and the connection properties are handled. Done means the job continues running without the "No operations allowed after statement closed" error after a connection becomes invalid.

Written by the indexing model from the issue text.