[JSWolf]

The problem is that you did not reference the fonts in the CSS. Here is a sample from one of my stylesheets from an ePub edited in Sigil.

@font-face {
font-family: Charis;
font-style: normal;
font-weight: normal;
src: url(../Fonts/CharisSILR.ttf);
}
@font-face {
 font-family: Charis;
 font-style: normal;
 font-weight: bold;
 src: url(../Fonts/CharisSILB.ttf);
}
@font-face {
 font-family: Charis;
 font-style: italic;
 font-weight: normal;
 src: url(../Fonts/CharisSILI.ttf);
}
@font-face {
font-family: smallcaps;
font-weight: normal;
font-style: normal;
src: url(../Fonts/CharisSILSmCp-R.ttf);
}
body {
font-family: Charis;
widows: 0;
orphans: 0;
margin-top: 0;
margin-bottom: 0;
margin-left: 0;
margin-right: 0;
text-align: justify;
font-size: 92.5%
}