We have had support for migration from S3-compatible storage for quite some time now, and we have heard that it has been working well for migrating from Amazon S3 and other compatible object stores.
However, GCS has some quirks in its AWS compatibility, which required some changes in our migration framework. That work is now complete and I am happy to report that we now support migration from GCS buckets as well. We have captured the steps for the migration in our documents at Migrating from a S3-compatible bucket | Tigris Object Storage Documentation.
Please reach out if you have any questions, or run into any issues.