According to the documentation open and close are still beeing used:
https://docs.flightsimulator.com/html/index.htm#t=Programming_Tools%2FSimConnect%2FAPI_Reference%2FGeneral%2FSimConnect_Close.htm
https://docs.flightsimulator.com/html/index.htm#t=Programming_Tools%2FSimConnect%2FAPI_Reference%2FGeneral%2FSimConnect_Open.htm
But they are not part of the DLLs and are depreacted based on this post:
https://docs.flightsimulator.com/html/index.htm#t=Programming_Tools%2FSimConnect%2FProgramming_SimConnect_Clients_using_Managed_Code.htm
Please update the Documentation 
The original functions are part of the DLL used from C++ but they are
encapsulated in the managed DLL - the pages you gave links to already explain
this so I am not 100% sure how you would like us to update the documentation.
Can you elaborate on this? Best regards, Eric / Asobo
If you start looking directly in the SimConnect API Reference
(https://docs.flightsimulator.com/html/index.htm#t=Programming_Tools%2FSimConnect%2FSimConnect_API_Reference.htm)
they are listed as working and if you then follow the tree down to the
Functions they are listed there as well. The only word that they are
deprecated is in the Notes on .NET
(https://docs.flightsimulator.com/html/index.htm#t=Programming_Tools%2FSimConnect%2FProgramming_SimConnect_Clients_using_Managed_Code.htm)
It would be good to have the “deprecated for managed SimConnect” directly in
the API Reference. So if later some stuff is “different” between both APIs it
is visible directly in the Page for each method. Or add a “copy” of the API
reference for the manged SimConnect Part as well.