There is currently an open issue about this here: https://github.com/dotnet/SqlClient/issues/30 The old assemblies can still be used in .NET Core, but only on windows machines, and with other limitations. (details are available in comments on the issue).
However since there's been no substantive movement in the 3 years since this issue was opened, if you're unable to use the existing native assemblies then your best bet is probably to output the data to a 3rd party nuget that has the functionality you need. https://github.com/DotSpatial/DotSpatial and https://github.com/GeoJSON-Net/GeoJSON.Net are both referenced in the SqlClient Issue, with GeoJSON.NET apparently being able to import and export while converting with geography.STAsBinary()
on the sql server side.