There is no official Mi PC Suite download for Linux, as the software is developed exclusively for

Shared Clipboard: Copy text on your phone and paste it on your Linux desktop.

2. Screen Mirroring & Control: Scrcpy (The Powerhouse)

Mi PC Suite offered a laggy, low-resolution screen mirror. Scrcpy (pronounced "screen copy") is dramatically better.

Your Linux machine and your Xiaomi phone were meant to work together. You just needed the right, better tools.