Make sure you are on the mono branch of Outward (see above).
r2modman is a mod manager which is integrated with Thunderstore, and supports Outward along with other games. Thunderstore is a mod database which supports Outward. If you see the 'radio buttons', make sure to click the radio button titled Version X.X.X:mono (where 'X.X.X' is the highest version number you can see) to update to the correct version.
Select the drop down and select default-mono. From there, go to Manage Installation > Configure.
In order to use mods, you need to be on a Mono branch of Outward.