So I ended up going Ian Turton's suggestion, which is to use a plain WMS getfeatureinfo request and overlay it on the WMTS layer, here is the code for anyone needing a similar solution:
<!DOCTYPE html>
<html>
<head>
<title>WMTS Layer with WMS getfeatureinfo</title>
<link rel="stylesheet" href="https://openlayers.org/en/v4.6.5/css/ol.css" type="text/css">
<!-- The line below is only needed for old environments like Internet Explorer and Android 4.x -->
<script src="https://cdn.polyfill.io/v2/polyfill.min.js?features=requestAnimationFrame,Element.prototype.classList,URL"></script>
<script src="https://openlayers.org/en/v4.6.5/build/ol.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/proj4js/2.4.4/proj4.js"></script>
</head>
<body>
<div id="map" class="map"></div>
<div id="info"> </div>
<script>
ol.proj.setProj4(proj4);
proj4.defs('EPSG:27700','+proj=tmerc +lat_0=49 +lon_0=-2 +k=0.9996012717 +x_0=400000 +y_0=-100000 +ellps=airy +towgs84=446.448,-125.157,542.06,0.15,0.247,0.842,-20.489 +units=m +no_defs');
const proj27700 = ol.proj.get('EPSG:27700');
const center_point = [394108.6719, 331807.5317];
var wmsSource = new ol.source.TileWMS({
url: 'http://localhost:8080/geoserver/ui/wms',
params: {'LAYERS': 'Flood 3'},
serverType: 'geoserver',
crossOrigin: 'anonymous'
});
var parser = new ol.format.WMTSCapabilities();
var map;
fetch('http://localhost:8080/geoserver/ui/gwc/service/wmts?request=getCapabilities').then(function(response) {
return response.text();
}).then(function(text) {
var result = parser.read(text);
var options = ol.source.WMTS.optionsFromCapabilities(result, {
layer: 'Flood 3',
matrixSet: 'EPSG:27700',
crossOrigin: 'anonymous'
});
var layers = [
new ol.layer.Tile({
opacity: 1,
source: new ol.source.XYZ({
attributions: 'Tiles © <a href="https://services.arcgisonline.com/ArcGIS/' +
'rest/services/World_Imagery/MapServer">ArcGIS</a> 2018',
url: 'https://server.arcgisonline.com/ArcGIS/rest/services/' +
'World_Imagery/MapServer/tile/{z}/{y}/{x}',
crossOrigin: 'anonymous'
})
}),
new ol.layer.Tile({
opacity: 1,
source: new ol.source.WMTS((options))
})
];
var map = new ol.Map({
projection: proj27700,
layers: layers,
target: 'map',
view: new ol.View({
projection: proj27700,
center: center_point,
zoom: 6
})
});
map.on('singleclick', function(evt) {
document.getElementById('info').innerHTML = '';
var viewResolution = /** @type {number} */ (map.getView().getResolution());
var url = wmsSource.getGetFeatureInfoUrl(
evt.coordinate, viewResolution, 'EPSG:27700',
{'INFO_FORMAT': 'text/html'});
if (url) {
document.getElementById('info').innerHTML =
'<iframe seamless src="' + url + '"></iframe>';
}
});
map.on('pointermove', function(evt) {
if (evt.dragging) {
return;
}
var pixel = map.getEventPixel(evt.originalEvent);
var hit = map.forEachLayerAtPixel(pixel, function() {
return true;
});
map.getTargetElement().style.cursor = hit ? 'pointer' : '';
});
});
</script>
</body>
</html>