I wonder whether it is possible to attach search databases to a new Search Application in same farm/different farm ? I found all Microsoft articles only mentioned attach Search Application to "renamed" databases, which can understand that they are already databases of that application before
If you want to migrate farm from one environment to another environment, I suggest you could back up the search service application and restore it in another environment.
We can back up and restore search service application by PowerShell command or Central Administration.
And the two procedures can back up all of the search components including the databases, the search service configuration, and all of the index files.
Back up Search service applications in SharePoint 2013.
Restore Search service applications in SharePoint 2013