You can only transfer groups to organizations you own or are an admin.
Existing database URL and tokens will continue to work, but should update your application to use the new URL and token as soon as possible.
curl -L -X POST 'https://api.turso.tech/v1/organizations/{organizationName}/groups/{groupName}/transfer' \
-H 'Authorization: Bearer TOKEN' \
-d '{
"organization": "new-organization-name"
}'