It seems like you did find the correct documentation for backing up the date from a Filestore instance. Since those solutions are provided by partners(not Google Cloud Platform), I believe there is no such option currently available to control the backup via GCP's console(UI) or CLI. You need to refer documentations[
doc-1,
doc-2] provided by respective partners.
I believe you already knew the option to copy data from a Filestore file share that is mounted on a Compute Engine VM instance to a Cloud Storage bucket by using the gsutil rsync command. This is achievable with the help of Cloud Storage bucket and the details are
explained here. But this option might take some time depending on the number and size of files.