Well, first of all, I think we have to question this assumption of yours:

new music was more rare than today

It is certainly true that there was not a huge commercial music business the way there is now, a constant stream of products readily available on your radio or spotify. But there was certainly no shortage of new music available for those who clamored for it. Opera goers living in Venice in, let's say, the 1730s had the opportunity to see 103 newly composed operas (this based on the opera production database "Corago," which unfortunately doesn't let you link directly to search results, but I typed in city, year range, and limited the search to premieres of new music). If you are going to the theatre today, you are most likely hearing music composed a number of years ago, whereas the norm in the eighteenth century was to hear music composed that year when you went to the theatre (which isn't to say old productions were never revived, just that new productions were extremely common). Likewise, a place like England had a robust publishing industry that frequently printed collections of recent music often organized around specific genres (ie, collections of new minuets, or "favorite songs" from new operas). So there was absolutely a ton of music available to you. You just couldn't listen to it on repeat or have it played for you on the radio.

So now to the substance of your post, fads. When we look at the way people describe music from their own time, it's pretty evident that people considered there to be fashions that weaved in and out, and that music had to adapt quickly to fashions to be successful. In one of the century's landmark textbooks on composition (called Gradus ad parnassum and published in 1725), Johann Joseph Fux throws up his hands with regard to the question of how to compose an aria, writing,

What can I say about arbitrary music, which is subject to change every 5 years or so? I do not disapprove of this eagerness for novelty, but highly praise it. If a middle-aged man appeared today dressed in the clothes worn fifty or sixty years ago, he would certainly run the risk of ridicule. Thus music must be accommodated to the times, too (Fux 279).

Of course, it's very hard for us to listen to music from the 1730s compared to the 1740s and make meaningful distinctions. But this might speak to an inability on our part to make fine distinctions in music that they would have been able to. One thinks of Casca in Shakespeare's Julius Caesar who, when asked to report the words of Cicero, replied "those that understood him smiled at one another and shook their heads; but, for mine own part, it was Greek to me." Until you really get to know a musical style, all examples of it will sound the same. And even the biggest classical music fans couldn't hope to have the kind of intimate knowledge that "native speakers" had when this music was current.

Now, here's a weird thing about the eighteenth century. I mentioned that when you went to the theatre, it was normal for you to hear new music. But often the words were not new. Indeed, the opera poetry written by a guy named Pietro Metastasio were often set to music over and over again, sometimes 50 to 100 times! Imagine going to Phantom of the Opera and each time you went it was new music! In any case, this gives us an opportunity to watch music evolve over time, as we can select one of his texts and just see what people did with it.

You are in luck, because about 2 years ago, I did just this with an aria called "Se cerca, se dice." On this website, I have about 15 ~30 second clips from the beginning of a bunch of different settings of this aria, arranged in chronological order. Listening to these back to back gives you a really strong sense of what stays the same from year to year and what changes. For instance, we can hear that doing this aria as a "minor mode" aria is a really early "fad," and it becomes a major mode aria around the 1740s. We can also see things that emerge around 1760, like a tendency to put a prominent instrumental melody separating the word "rispondi" from "mori." This speaks to the way that instruments began to take on a more "independent" role, having their own melodies rather than just supporting the singer with chord tones as in earlier settings. We can also hear that the orchestra gradually grows: early settings are just strings, and the later we go, the more likely we are to find woodwinds and brass instruments. There are a ton of cool things about this aria and what it shows about history (this is what my dissertation is on), but it would be too much to get into right now. But hopefully this gives you some aural sense of how things change across history!

It's hard to know where to even begin with talking about musical fads, because each individual fad will have its own context and history. But in this response, I hope to have at least shown that people believed that music did follow fads in this time. I also hope to have attuned your ears to "subperiods" of eighteenth century music by watching one musical text realized by 15 different composers throughout the century.

This is about all I have time for as I travel for the holidays. If I had more time, I think I'd want to give you an example of a very specific "fad" and show its individual history and currency. Unfortunately, I simply do not have the time to do that adequately at the moment. I may reply to this comment in a week or so to provide that, or perhaps some other user has a fad immediately at hand they could provide you the history of. I definitely think that's a needed part of this answer, so hopefully one can be provided! Perhaps /u/vornska or /u/wysiwygh8r or /u/caffarelli would have a specific 18th century fad they could speak to.