This issue seems exclusive to Windows (it does not happen on Mac). I run three parallel Studio sessions each using the integrated MCP server. When Studio displays the button to update I close all but one Studio instance and click the button and I then receive the message about needing to close out all studio instances to update. I tried repeatedly closing and reopening the last Studio instance to no avail. So I went to task manager and typed in Studio and sure enough one Studio task and 3 MCP server tasks get orphaned. Killing them and then opening Studio and clicking the Update button then works.
Expected behavior
Maybe there’s a reason the MCP server instances can’t safely exit when their parent Studio session ends, but if that’s not the case, then I think the answer is to just clean up the orphaned task(s), when a Studio session is closed.