You don’t need to stop the application to upgrade the version, because MongoDB uses the rolling up strategy, doing it first on the secondary nodes and then on the primary, performing a failover.
Two points:
First, make sure that your application has retryReads and writes configured in the connection string so that when a node fails over or is upgraded, there are no errors and instead your app will retry.
Another point you need to evaluate is the compatibility of your connection driver with the features that the cluster will have in that version. There may be commands or operators that have been deprecated in the meantime that you use in the application and this may cause problems for you. If you ensure this, I don’t see any more problems with your upgrade =D