I have a similar issue with rule-based layers. QGIS2web is exporting them and I can see them all in the "layers" folder, but they are not displayed. I checked the HTML file that links to the .js files in the "layers" folder created by QGIS2web, and I can see that one of the layers is referred to correctly:
<script src="resources/proj4.js"></script>
<script>proj4.defs('EPSG:3857','+proj=merc +a=6378137 +b=6378137 +lat_ts=0 +lon_0=0 +x_0=0 +y_0=0 +k=1 +units=m +nadgrids=@null +wktext +no_defs');</script>
<script src="resources/polyfills.js"></script>
<script src="./resources/functions.js"></script>
<script src="./resources/ol.js"></script>
<script src="./resources/ol-layerswitcher.js"></script>
<script src="layers/mossdepotsformerlygeneralsupply_1.js"></script><script src="layers/generalsupplydepots_2.js"></script>
<script src="styles/mossdepotsformerlygeneralsupply_1_style.js"></script><script src="styles/generalsupplydepots_2_style.js"></script>
<script src="./layers/layers.js" type="text/javascript"></script>
<script src="./resources/Autolinker.min.js"></script>
<script src="./resources/qgis2web.js"></script>
The other layers do not come up in the HTML file at all. And not even the layer I can see here is displayed on the actual map. All my layers are rule-based and some of them contain rather complicated expressions.
What I will do now is extract all the layers I need as separate GeoJSON files from my original data set using Python, but with this pre-selection, it will be inconvenient to highlight different attributes in the same map at a later stage.