I'm not sure this is feasible. Solargraph starts whenever the extension gets activated, most often because a Ruby file was opened in an editor. There's some overhead involved in starting the language server, so once it's initialized, it stays open for the duration of the session. This is typical behavior for all language servers. (If you mean the language server keeps running after you close VS Code altogether, that's a different issue.)
What OS, Ruby version, and Solargraph version are you using? (You can get a lot of information about your environment by running "Solargraph: Get environment info" from the VS Code command palette.)
Can you give me a reproducible example of a workspace that leaves Solargraph running after you close VS Code?
I'm not sure this is feasible. Solargraph starts whenever the extension gets activated, most often because a Ruby file was opened in an editor. There's some overhead involved in starting the language server, so once it's initialized, it stays open for the duration of the session. This is typical behavior for all language servers. (If you mean the language server keeps running after you close VS Code altogether, that's a different issue.)