If a device provider fails to start (for instance the pulseaudio provider unable
to connect to the PulseAudio daemon) then the monitor should not keep track of
it in its `started` providers list. Otherwise a false positive critical warning
would be raised.
This patch also switches the started_count type from bool to int, for
consistency. This is a counter, after all.
API: gst_device_provider_is_started
Part-of: <https://gitlab.freedesktop.org/gstreamer/gstreamer/-/merge_requests/679>