After invoking the Spring Boot: Set Log Levels action from the command palette, the running Spring Boot app that is already connected to the live hovers system shows up twice.

In the regular Manage Live Spring Boot Process Connections menu, there is two items for the running and connected app as well, but those two items serve a different purpose: Refresh and Disconnect. Looks like the log levels quick pick re-uses a similar logic, but seems to ignore the fact that it is all about the same process.