I haven't married Elliott yet but I've married Haley and Penny and am eyeing up Alex, and Elliott is like the best of all of them mixed together so I'm totally going to give an uninformed opinion.
If you've just married him, then this is consistent with married behavior for some spouses. Single Haley doesn't do much in the regular game though she goes out to the Park and the Beach depending on the season, but she doesn't have a complex behavior set. Which means that married on the Farm, she has even less to do though she does go to town on occasion, but she doesn't have a job or other motivation. So um, yeah. She stands around the house looking at things.
A lotta spouses do that, it's kinda dull.
I think the impression the Farmer's supposed to have is their spouse does many of the typical things they'd do when single but instead in the Farmhouse. And do it when you're out and about so you just miss it? IMO it would be great if you'd see Elliott at a writing desk, working. Or Haley in a darkroom at the back of her room (this doesn't exist in-game but should). I would love to see Penny sitting on a couch if you place one facing south or even on the floor of her room reading. The sprites are already in the game, why not? Penny continues to go to town to tutor the kids which is nice, but adding a natural married behavior in the Farmhouse matching their single behavior would be a very nice detail.
Also, looking at your minimalist design aesthetic, Elliott doesn't have much to look at so I wouldn't be surprised that the Catalog is among the best options for the game to choose. If you fill your house with the statues and reward things, even the vases of Flowers you can get from the Catalog and Festivals, he will look at those things, choosing among them at different times during the day.
OK! OKokok here's an idea: design a little something for Elliott in the house from the stuff you can choose in the Catalog. Part of a room, anything, maybe just a reading nook. Just give him something fun to look at! Maybe that can help with design if you're looking for inspiration.