Classical music for small ensemble is called Chamber Music. It's typically instrumental, but there are compositions for what would be called "Voice with Chamber Ensemble." This link gives several examples: https://www.talkclassical.com/12105-chamber-music-featuring-voice.html
Here are a couple links I found using that as a search term, but the vocals aren't quite as naturalistic as you're seeking. Unfortunately the highly trained vocal approach you're calling "opera style" is the standard for classical music.
Elegy for Voice, Flute and Piano
From the Japanese Poetry
As @Angst identified, if you really want the naturalistic vocals, you'll probably have to go all the way back to the pre-classical era, to what's called "Early Music". Here's a good mix I found using the search term "early music female vocal" (although it's really more "medieval-style" than actually authentic).
Finally, if you're not wedded to a classical style, you might enjoy female-fronted New Age music like Loreena McKennit and Enya or even Chamber Pop music like San Fermin, Girls in Trouble and Regina Spektor.