You need to make sure in VS2019 that the TargetServerVersion property setting value on the project level is matching your SSIS run-time version, i.e. SQL Server2016
Please make sure that you are running latest versions of both (1) VS2019 (v.16.7.5) and (2) SQL Server Integration Services Projects for VS 2019 (v.3.10). The (2) is an extension for VS2019.
There is no need to install SSIS extension 3.10 on the SQL Server 2016 side. It is just for Visual Studio.