I downloaded Slime Rancher on a new system and my saves are missing

The save files for Slime Rancher are stored locally, so unless you set up any sort of cloud saving, they will still be on your old system. If you have access to it, you can find them in the following locations, and manually transfer them to your new system:

Windows

C:\Users\[username]\AppData\LocalLow\Monomi Park\Slime Rancher

Mac

Macintosh HD\Users\[username]\Library\Application Support\Monomi Park\Slime Rancher

Linux

.config/unity3d/Monomi Park/Slime Rancher