This script behaves as expected.
<script>
let cadena = "soy una cadena";
let cadenaI = cadena.split("").join("/");
console.log("soy cadenaI: "+cadenaI);
</script>
This second script does not run as expected, being apparently the same:
<script>
let cadena2 = "soy una cadena";
let cadena2I = cadena.split("");
cadena2I.join("/");
console.log("soy cadena2I: "+cadena2I);
</script>
You are not saving the result of the join operation in any variable, so you are showing the result of the split in the console. Save the result in a new variable and you can display it.