The error "Cannot obtain Oracle Client information from registry" means that you don’t have Oracle client installed or the bitness of your application doesn't match the bitness of your Oracle Client.
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(Example for x32)
1.) Make sure that "Platform target" of your application has value "x86" (not "Any CPU")
2.) Install x32 Oracle client
https://www.oracle.com/database/technologies/instant-client/microsoft-windows-32-downloads.html
3.) Make sure that the path to this client in the path environment variable is the very first (if there are several clients). Or set ORACLE_HOME environment variable.
4.) Create the correct TNS for your ORACLE server in the file:
%ORACLE_HOME%\instantclient_19_10\network\admin\tnsnames.ora
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(Example for x64)
1.) Make sure that "Platform target" of your application has value "x64" (not "Any CPU")
2.) Install x64 Oracle client
https://www.oracle.com/database/technologies/instant-client/winx64-64-downloads.html
3.) Make sure that the path to this client in the path environment variable is the very first (if there are several clients). Or set ORACLE_HOME environment variable.
4.) Create the correct TNS for your ORACLE server in the file:
%ORACLE_HOME%\instantclient_19_10\network\admin\tnsnames.ora