I believe technical support is in the process of reaching back to you on this issue. The first check is to see whether the versions of both products match to the first decimal, which is a necessary condition for the link to work.

For the link between Mathematica version 12.1.1 and System Modeler version 12.1.0, the following can help

PacletDisable /@ PacletFind["WSM" -> "12.2.0"];
PacletDisable /@ PacletFind["WSMLink" -> "12.2.0"];

systemModelerInstallationPath = "/usr/local/Wolfram/SystemModeler/12.1/";
PacletDirectoryLoad[FileNameJoin[{systemModelerInstallationPath, "Mathematica"}]]

, where systemModelerInstallationPath should be adapted to match the installation path of System Modeler on your machine. The PacletDirectoryLoad is per session, while the PacletDisable is permanent, so the PacletDirectoryLoad lines can be placed in Kernel/init.m inside $UserBaseDirectory. Alternatively, they can be evaluated manually once at the beginning of every kernel session.

Another possibility is that the compiler for System Modeler has not been properly configured, see https://reference.wolfram.com/language/tutorial/CompilerForSystemModeling.html

Was able to solve it.

Thank you again!