When trying to pull / push from a branch I add no other message than "Start a code editing session ...."
The start code editing session did not produce any result.
When running the extension from source I discover that the "initializeFlutter" method was not performing correctly.
After running manually the command : fvm use 3.27.3 -f "MY_PROJECT_PATH" it solved the issue.
My guess is that when the correct flutter is not install the initialization failed since fvm command asked for confirmation before downloading the correct version.
Maybe a specific error message could be display to the user to inform him that he should install the flutter version.