refactor: use 1 db pool instead of 3

internal/eventstore/repository/sql/query.go

@@ -309,7 +309,7 @@ func prepareConditions(criteria querier, query *repository.SearchQuery, useV1 bo
 		}
 
 		for i := range instanceIDs {
-			instanceIDs[i] = dialect.DBPurposeEventPusher.AppName() + "_" + instanceIDs[i]
+			instanceIDs[i] = "zitadel_es_pusher_" + instanceIDs[i]
 		}
 
 		clauses += awaitOpenTransactions(useV1)

internal/eventstore/v3/push.go

@@ -4,9 +4,11 @@ import (
 	"context"
 	"database/sql"
 	_ "embed"
+	"fmt"
 
 	"github.com/zitadel/logging"
 
+	"github.com/zitadel/zitadel/internal/api/authz"
 	"github.com/zitadel/zitadel/internal/database"
 	"github.com/zitadel/zitadel/internal/eventstore"
 	"github.com/zitadel/zitadel/internal/telemetry/tracing"
@@ -55,6 +57,11 @@ func (es *Eventstore) writeCommands(ctx context.Context, client database.Context
 		}()
 	}
 
+	_, err = tx.ExecContext(ctx, "SET LOCAL application_name = $1", fmt.Sprintf("zitadel_es_pusher_%s", authz.GetInstance(ctx).InstanceID()))
+	if err != nil {
+		return nil, err
+	}
+
 	events, err := writeEvents(ctx, tx, commands)
 	if err != nil {
 		return nil, err