According to the website Putting the Emerald in Emerald Lake – Where do the colours come from?, the reason for the colour is the same that occurs in lakes, it is due to what is known as or similar material to 'rock flour' - consisting of
of fine-grained, silt-sized particles of rock, generated by mechanical grinding of bedrock
and relevant to a river environment
When the sediments enter a river, they turn the river's colour grey, light brown, iridescent blue-green, or milky white.
The colour is due to:
the suspended material distorts the wavelengths of light, reflecting back more of the green and blue end of the spectrum
These usually originate from glacial melt, even though there are no glaciers in the Julian Alps presently, but there used to be, resulting in according to the WP6 Hydro-geological upgrade and improvement of the GIS of the sources of drinking water webpage as having
The intergranular aquifer in the alluvium of the Soča/Isonzo River, which is composed of fluvial and fluvioglacial gravel and sand sediments with individual lenses of conglomerates
further explained in the article Bovec basin (Upper Soča valley, Slovenia), as having
sediments are represented from bottom to top by partly lithified glaciofluvial sediments, overlain by lacustrine
chalk. During the Holocene, the chalk was partly eroded (in some areas totally) and covered by glaciofluvial
sand and gravel which are weakly cemented in some parts into conglomerate and by unconsolidated moraine
Potentially, plenty of source material. The particles are small enough to be suspended in the water of the Soča River.