I created a "project from existing files" via sftp, and excluded some logfiles from syncing. Now I uploaded some new folders to the server - how can I get PhpStorm to download and index them?
Use Remote Host side panel.
If you do not have it -- use Tools | Deployment | Browse Remote Host to bring it up.
Browse your remote system using it and choose Download from here from context menu. If such action is not available then you have some misconfiguration -- e.g. that path is excluded from deployment or not mapped at all.
Alternatively you may use Deployment | Sync with deployed... -- it will check for differences between local and remote (may take time if connection is slow or you have lots of files).