You shouldn't add any mods which aren't made for your SPT version. If a mod has a red or grey tag, and you are on the latest main SPT release (current one being 3.9.X), then do not install it.
Recoil Overhaul is made for SPT 3.7.X. Don't install it and your game will work fine. Loot Radius should work fine.
The server window will only show mods that are installed in the User/mods folder. The F12 menu will show mods in the BepInEx/plugins folder (if they have a F12 menu entry).
Ok, great, turns out that was it. Thanks for the help!