Hey guys. Sorry for my english, but i have problem.
Installed clean rust server from steamcmd. Then, downloaded latest linux build from this page: https://umod.org/games/rust
After installing oxide, server can't start with error flood in console:

Server Exception: Steam Query 
(Filename: ./Runtime/Export/Debug/Debug.bindings.h Line: 35)

FileNotFoundException: Could not load file or assembly 'Facepunch.Steamworks.Win64, Version=*.*.*.*, Culture=neutral, PublicKeyToken=null' or one of its dependencies.
  at ServerMgr.Update () [0x00109] in <2dba29a1f66640cc926784c4e56cd653>:0 
UnityEngine.DebugLogHandler:Internal_LogException(Exception, Object)
UnityEngine.DebugLogHandler:LogException(Exception, Object)
UnityEngine.Logger:LogException(Exception, Object)
UnityEngine.Debug:LogException(Exception, Object)
ServerMgr:Update()
​

Seems like wrong build placed in https://umod.org/games/rust/download/develop  (not for linux). What's wrong?

That download is correct and is providing the right build. All I can suggest is to make sure that is the build you are using. The filename would be Oxide.Rust-Linux.zip.