1.Use PowerShell to back up search in SharePoint Server.
Backup-SPFarm -Directory <BackupFolder> -BackupMethod {Full | Differential} -Item "Farm\Shared Services\Shared Services Applications\<SearchServiceApplicationName>" [-Verbose]
2.Use Central Administration to back up search in SharePoint Server.
Go to Central Administration -> Backup and Restore -> Perform a backup -> Expand Shared Services -> Expand Shared Services Applications -> Select the search service application -> Select Backup Type -> Fill in Backup File Location.
Reference:
https://learn.microsoft.com/en-us/sharepoint/administration/back-up-a-search-service-application
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