Migration from another OS to Linux
The Linux server will have a new identity. Plex will consider it a new server.*
Account information is stored with the account at plex.tv, not on the server.
If you share libraries with others, you will have to share them from the new server. You will not have to re-invite anyone. They will have to pin the new libraries to their home pages.
If the Windows & Debian systems both have access to the media, you can run both servers at the same time, migrating over when you deem the new server is stable. This will also let others migrate when they are ready to do so (no hard cutover).
Enable Sync Watch State & Ratings to keep the information synchronized between servers. It is an account, not server, setting. Anyone you share with should enable it as well (Managed Users are not supported).
* Each Plex server has a unique identity (like an ID number). On Windows systems, the information is stored in the Windows Registry. On Linux systems, it is stored in the preferences.xml file in the Plex Data Folder.
When moving between systems on the same operating system (ex: Win to Win, Linux to Linux), it is easy to keep the identity by copying the information between Windows Registries or copying preferences.xml to the new system. The new system is essentially a clone of the old system (and the two cannot be running at the same time).
Moving to a new system on a different OS is more problematic. There is no tool to copy the information between Windows Registry and preferences.xml (or vice-versa). Instead of manually copying the information, most people bring up the new server as a new system with a new ID and name. The downside is the need to share libraries again. The upside is you can run both servers at the same time, migrating users when convenient.
