I was able to work around this issue and Playdate Simulator debug adapter protocol does not send success response to launch request by proxying messages to and from the Simulator: https://github.com/midouest/vscode-playdate-debug/blob/main/src/PlaydateDebugAdapterProxy.ts
Patching the supportsTerminateRequest property now causes VS Code to correctly terminate the debugger when the user clicks the stop button.