Did it originate with an intentional propaganda campaign by the Nazis, or did it happen later?
It's a complex development, but I'll do my best to briefly summarize some key points.
Let's start with a quick bit of background: Runes developed as a writing (or, rather, carving) system among the ancient Germanic peoples during the Proto-Germanic period ultimately based on scripts form the south, and were subsequently employed in various forms by Old English speakers, Old Norse speakers, and speakers of extinct Germanic languages such as Gothic. Generally speaking, these peoples continued to carve runes for a variety of purposes until the script was superseded by Latin characters under Christianization. Runic scripts fell out of general use but didn't exactly disappear; they continued to be used for specialized purposes here and there in Scandinavia, for example. The academic study of runes is known as runology, a subfield of ancient Germanic studies which requires a substantial familiarity with topics such as historical linguistics and other relevant areas of anthropology. Scandinavian runestones are the best known examples today, but new runic inscriptions are found pretty regularly and sometimes attract some media attention. (It’s important to note here that the vast majority of runic inscriptions were doubtlessly carved into wood and therefore would have either become quick fuel or simply biodegraded long ago.)
Anyway, without casting too wide a net, the 19th century saw a lot of innovation in the humanities. Developments in linguistics, particularly with the discover of what we nowadays know as Grimm's Law, made major waves. This led to a wellspring of discoveries regarding history and language, as well as the development of early forms of numerous fields that still exist today, such as the closely entwined fields of historical linguistics and folklore studies. Some of these understandings were in a primitive state, while some were closer to where we are today, but this material filtered down to a surprisingly wide audience by way of individuals such as philologist Max Müller.
For what would become Nazi runic iconography in particular, Guido Karl Anton List, known later in life as Guido von List, would play an outsized role. Von List was a journalist and a writer closely involved in Austrian nationalist circles focused on notions of ‘Pan-Germanism’, and close to the end of his life he was influenced by theosophy in particular, a new religious movement. During this time he formulated a bunch of pseudoscientific notions about runes and language, and was in contact with similarly-minded individuals, such as Austrian former Catholic monk Jörg Lanz von Liebenfels (born Adolf Josef Lanz).
As their adaptation of the name element von implies, denoting descent from nobility, both figures maintained ideas of descent from some kind of ancient nobility, and both promoted a form of ‘ancient Germanic’ monotheism that involved intricate and fantastical concepts of supposed ancient peoples combined with other pseudoscientific ideas about race and templars and imagery from the ancient Germanic peoples and all sorts of other out-there stuff. Von List espoused the idea that ‘twelve gods’ developed from ‘one god’ (hypothesizing a sort of corruption of monotheism among the ancient pagans), von Lanz fixated on the ancient Germanic (and beyond) symbol of the swastika. And, uh, animal-people hybrids. Von Lanz called the beliefs he espoused ‘Theozoology’ or ‘Ario-Christianity’, while Von List referred to his beliefs as Arminism. Both were distinctly inspired by mystery religions and secret societies, and both used imagery that trickled down from academia about the pre-Christian Germanic record combined with concepts and imagery from Christianity.
As you can imagine, none of this stuff is particularly coherent, but it all fed into a soup of related völkisch cultural stuff that had a significant impact in Austrian and German nationalist circles, sometimes reaching to high status individuals with real influence. Importantly for future Nazi iconography, von List developed a runic script he called the Armanen runes. By way of Nazi figures such as Karl Maria Wiligut and Heinrich Himmler, von List’s influence, although quite limited, would pop up later in Nazi iconography. Von List’s impact here is most apparent in the names of some of the runes used in Nazi iconography.
As for historic ancient Germanic imagery, now and then one encounters this in Nazi iconography as well, but with notable limitations. It’s very rare to encounter any kind of, say, depiction of ancient Germanic deities, but one will encounter other, seemingly random things inspired by the historic record, like the slave-labor made Julleuchter decorations, as well as a wide variety of stuff essentially fabricated (like Ahnenerbe member Wilhelm Teudt’s supposed “Irminsul” symbol). In ancient Germanic studies under Nazi Germany, pseudoscience reigned, and scholarship in the humanities was severely stunted, to say the least (see throughout Mees 2008 for numerous examples and discussion).
That said, it’s easy to overstate exactly how much presence this stuff had in Nazi Germany, and this topic has been the subject of much sensationalization. Germany was very much a protestant and Catholic nation, which came with religious institutions that aided and abetted Nazi Germany’s development (see, for example, Heschel 2008), and imagery derived from that heritage was extremely common (for example, Nazi Germany continued the tradition of the use of ‘Gott mit uns’ on military belt buckles, deriving from Matthew 1:23). In Nazi Germany, debate could occur on certain topics relating to ancient Germanic history, resulting in, say, heated discussion over whether Charlemagne should be seen as a Germanic (albeit Frankish) national hero or a butcher of the ancient pagan Saxons for refusing his rule, but invariably the decision would come down on the side of the Christian conquerer, leading to Nazi Germany’s embrace of Charlemagne as a heroic figure that some Nazi textbooks compared to Hitler. Charlemagne’s supposed birthday anniversary in 1942 was celebrated with a postage stamp.
Just as interesting is the post-World War II media fixation on the ‘occult’ elements of Nazism over ‘mainstream’ Nazi beliefs, which has created something of a cottage industry for genres of fiction and other forms of media, such as video games, where the Nazis draw from ‘dark occult’ powers, rather than the very real social, religious, and political factors that led to Nazi Germany. A lot of elements central to Nazi ideology, such as persecution of Jews, were nothing new, reaching back well into the medieval period in the region. Comparatively little regarding everyday Nazi Christianity in the Third Reich has made it into pop culture media, which often prefers to sensationalize these ‘occult’ aspects and 'exotic' ideas, such as symbolism derived from ancient paganism.
For further reading in English, I recommend a combination of the following sources:
* Goodrick-Clarke. 1993. The Occult Roots of Nazism. NYU Press.
* Heschel, Susannah. 2008. The Aryan Jesus: Christian Theologians and the Bible in Nazi Germany. Princeton University Press.
* Mees, Bernard. 2008. The Science of the Swastika. Central European University Press.
Edit: Typos