Error handling is not SQL Server's best game. And it only gets worse if you add linked servers to the mix. I have a series of articles on error handling on my web site, and there an appendix that covers linked servers, https://www.sommarskog.se/error_handling/Appendix1.html. It's quite scary.
When you see this particular error message, A severe error occurred on the current command. The results, if any should be discarded., this indicates that there has been an internal error of some sort. If the severity level is 20, it was an internal error in SQL Server, and your connection was cut. You would also find an error message in the SQL Server error log.
In you case, the severity level is 11, which indicates that the error occurred in SqlClient, the client API that SSMS uses. However, I believe that most of the time you see this error, SQL Server is sending illegal TDS.