Processes don’t share an appdomain, in .net core, each process supports one “appdomain”.
In the old framework, an appdomain was an isolation tool. A process could host multiple appdomains and they could communicate with each other via marshaling. An appdomain could be unloaded. This was commonly used for plugin architecture. The plug-in could crash without hurting other host domains. Domains could load other domains. So they could be controlled with c# code.
None of this support was added to .net core. Instead they have focused on loading and unloading assemblies similar to c/c++
In reality there is no real appdomain support in .net core. .net core is runtime hosted by an application.