feat: add program name to MySQL connections (#1617)

## Description

---
Audit your applications by using the following sql to track program name
```
SELECT
    session_connect_attrs.ATTR_VALUE AS program_name,
    processlist.*
FROM
    information_schema.processlist
LEFT JOIN
    performance_schema.session_connect_attrs
ON
    (processlist.ID = session_connect_attrs.PROCESSLIST_ID AND session_connect_attrs.ATTR_NAME = "program_name");
```


## PR Checklist

---
> Thank you for opening a Pull Request! Before submitting your PR, there
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[CONTRIBUTING.md](https://github.com/googleapis/genai-toolbox/blob/main/CONTRIBUTING.md)
- [ ] Make sure to open an issue as a

[bug/issue](https://github.com/googleapis/genai-toolbox/issues/new/choose)
before writing your code! That way we can discuss the change, evaluate
  designs, and agree on the general idea
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🛠️ Fixes #<issue_number_goes_here>

internal/sources/cloudsqlmysql/cloud_sql_mysql.go

@@ -118,9 +118,8 @@ func initCloudSQLMySQLConnectionPool(ctx context.Context, tracer trace.Tracer, n
 			return nil, fmt.Errorf("unable to register driver: %w", err)
 		}
 	}
-
 	// Tell the driver to use the Cloud SQL Go Connector to create connections
-	dsn := fmt.Sprintf("%s:%s@cloudsql-mysql(%s:%s:%s)/%s", user, pass, project, region, instance, dbname)
+	dsn := fmt.Sprintf("%s:%s@cloudsql-mysql(%s:%s:%s)/%s?connectionAttributes=program_name:%s", user, pass, project, region, instance, dbname, userAgent)
 	db, err := sql.Open(
 		"cloudsql-mysql",
 		dsn,

internal/sources/mysql/mysql.go

@@ -24,6 +24,7 @@ import (
 	_ "github.com/go-sql-driver/mysql"
 	"github.com/goccy/go-yaml"
 	"github.com/googleapis/genai-toolbox/internal/sources"
+	"github.com/googleapis/genai-toolbox/internal/util"
 	"go.opentelemetry.io/otel/trace"
 )
 
@@ -122,7 +123,11 @@ func initMySQLConnectionPool(ctx context.Context, tracer trace.Tracer, name, hos
 		values.Set(k, v)
 	}
 
-	dsn := fmt.Sprintf("%s:%s@tcp(%s:%s)/%s?parseTime=true", user, pass, host, port, dbname)
+	userAgent, err := util.UserAgentFromContext(ctx)
+	if err != nil {
+		return nil, err
+	}
+	dsn := fmt.Sprintf("%s:%s@tcp(%s:%s)/%s?parseTime=true&connectionAttributes=program_name:%s", user, pass, host, port, dbname, userAgent)
 	if enc := values.Encode(); enc != "" {
 		dsn += "&" + enc
 	}