TBH I'm not at all sure of the spacing required. If there is not enough space elsewhere, a house can clip into a path. let alone sit right up next to it.
I've seen posts where players say how to place the tiles/patterns - almost like a chess board, say all the white squares you place as patterns.
Do houses need a space bigger than a 3x3 to plot - yes they might, this is where I'm hazy, its not been an issue for me as I'm not trying to put houses into exact spaces or into straight lines. (would have to search on this point - I'm pretty sure there has been BTF posts on this).
My problem has been my eyes see trees & flowers as permanent, its best to move hybrids - say to the beaches and tile around trees.
It is time consuming, tho I haven't found it unbearable, its partly as I try to combine tiling 'no go' areas with plot resetting, and I'm not overly picky as to where a villager plots.
Quick search: a villagers house needs a 5x5 space as they won't plot within 2 spaces of say a rock or building (civic or houses), but they will plot nearer than this to the plazas.
Ragdoll's post is also relevant:
https://www.belltreeforums.com/showthread.php?310996-The-precision-of-villager-plot-resetting