You're on the right path, Intersection() works when you're working with 2 individual geometries, whereas in your instance it's 1 geometry with a collection (even though your collection is only 1 intersecting geometry)
I suggest digging into the resulting intersects result using:
var intersectsResult = Intersects($feature, otherLayer);
if (Count(intersectsResult) == 1) {
// Run Intersection and the result will be the intersecting point geometry
var intersectingPoint = Intersection($feature, Geometry(First(intersectsResult )));
} else {
// There's more than 1 intersecting line, do nothing
return null;
}
If you do want to work with multiple intersecting lines, using a for loop() will allow you to cycle through the results and work with each intersecting point geometry like line 5.