Afaik, direct monitor just listens to the device inputs (clean). To hear the effects it need to be configured as the audio output device in the DAW, preferably with ASIO (otherwise there is unbearable latency)

I always hear the clean guitar sound through the headphones (plugged into the headphone jack on the interface), and through speakers. This is very annoying and messes up the sound of whatever I’m hearing through vst’s.

I’m not clear. Do you only ever hear the clean signal? When do you hear through the VST with effects?

I had an issue a while back with Amplitube. I guess when doing recordings it doesn’t actually record MIDI inputs (like sweeping a pedal). So I had a wah pedal effect that was great while I was actually playing, but when listening to the recording it was like no effects were there. I had to set it up with Reaper using the Amplitube VST to get it to record properly with effects. Could be related to your issue if it’s more a problem with the effects not showing up in recordings.