Upon further testing, I found out that
Red Brick Wall, Large Red Brick Wall, Medium Gray Brick Wall, Large Grey Brick Wall, and Medium Tiled Roof Column still clip into each other just fine (these are the Haranya-inspired brick walls). You can see how they can be connected to slightly clip into each other on this image.
This is how all the other walls used to work too.
View attachment 28613
So the list of the walls that don't work like that anymore is actually much shorter, it's just
Short Grass Fence, and the Nuia-inspired brick walls:
Short Brick Wall,
Brick Wall,
Medium Brick Wall,
Large Brick Wall,
Decorative Spiked Iron Gates and
Decorative Tapered Column.
The same applies to their Crest and Golden Carp variants, as well as the bound variants of these, and the Mossy Rock walls. The Crest walls also have an additional issue - they don't stand up straight regardless of the terrain like the other walls do, they behave more like furniture and follow the terrain slopes when it's uneven.
View attachment 28612
Essentially, all walls should behave the same as the Red Brick Wall still does, so that they can be slightly clipped into each other to fully connect them (which was possible from the launch of the game up until a certain patch a few years ago).