Perhaps I'm wrong and Element can in fact be a Textual node. Regardless, I have an Element whose toString() says <template class="header"> Name </template> (it's basically Grid's header made sortable), but calling getTextRecursively() on this element returns an empty string.

Workaround: This Kotlin code works properly.

val Element.textRecursively2: String get() {
    val node = ElementUtil.toJsoup(Document(""), this)
    return node.textRecursively
}

val Node.textRecursively: String get() = when (this) {
    is TextNode -> this.text()
    else -> childNodes().joinToString(separator = "", transform = { it.textRecursively })
}

We have a bunch of tests in com.vaadin.flow.dom.ElementTest that assert that getTextRecursively() returns various non-empty values.

The reason in your case is most likely that the <template> element is configured with an innerHTML property instead of having a proper text node child. <template> elements work in a special way in the browser, so regular child elements are ignored. We must instead pass the contents as innerHTML to make it work.