What you see there is z-fighting, so what you’re trying can be better archived by keeping those grassy details inside your tile - but making it seamless to the neighbour tiles which is perfectly possible for your pattern. You can set
alphaTest: 0.5 in your material to reduce the black border, but it won’t help with z-fighting which will be only a little less visible as the colors are similar.
To get overlapping on the edges/cliffs like in your first picture you can use a set of 4 tiles wich have only 1 side with the grass overlapping each.
Another approach is using decals, for decals there are a couple methods, but archiving transparent ones which aren’t projected on a geometry is harder as you’re again have to avoid z-fighting. One thing in this regard helping is using a logarithmic depth buffer and a minimal offset increasing by distance - but remember enabling
logarithmicDepthBuffer for the renderer will also come with a cost and rather pays off when your scene renders large distances and therefore requires it.