Why did my 35mm scans come out with this white grain?

Your first image is incredibly underexposed. Grainy + grey/lack of contrast on color negative films is the dead giveaway for underexposure.

Your second image looks properly exposed and the color and contrast look to be what I'd expect with Portra 400 shot midday-ish in hard sun.

I don't think there is a gear/film issue here. ISO400 film is not fast enough for hand-held shutter speeds at night or in dim lights. Interiors may look bright to your eyes, but they actually have very, very little light when compared to outside.

You need to work on your metering and make sure that you are exposing the film properly. With color negative film, err on the side of overexposure as they'll tolerate a few stops overexposure with ease, not blowing the highlights...but even just a stop underexposed and they start to get grainy and lose contrast.

If you want more saturated colors, then you need to shoot when the lighting is better. Golden hours are good, as are overcast days. The hard, bright sun during midday tends to wash everything out. But, it can make for some great tonal shifts in a black and white image, so consider carrying black and white film as well.

Additionally, you can switch films. Portra 160 and Ektar 100 are both pretty punchy. Fuji Pro 400H is good as well, and Fuji Velvia is incredibly saturated - though it is a color reversal film, not color negative. Though films have differing characteristics, you'll see the most dramatic change in saturation captured by exposing your film correctly and shooting in softer lighting conditions.