Apparently the restaurants that YOU think are fancy in your area like jazz.

High cost “fancy” restaurants do not all play jazz.

For example just last night I was at the Waffle House and the cook had on Rob Zombie’s American Made Music to Strip By.

The waffles were five star.

This is a loaded question in so many ways. You may be confusing other genres like lounge and bossa nova with jazz. In general you'll find easy listening music, and smooth jazz is included in this. But I don't expect you'll hear other kinds of jazz like modal jazz, free jazz, jazz fusion, and so on.

Typically you want music that's quiet, low or mid tempo, free of vocals, and does not consist primarily of music made with synthesizers (as older people may find this to be a turnoff, even if it's peaceful music). I have a feeling that a good portion of this is (other than classical music, as mentioned in another comment) being categorized as "jazz" to you because you may not be familiar enough with a large variety of music.

Also I can give you a piece of advice. If you are in charge of creating a playlist at an upscale Italian restaurant in San Mateo, California, working part time minimum wage as a line cook, and your boss says, "Hey, you have long hair, you probably know a lot about music, right?" you should not choose your personal, pre-existing playlist that consists of every song in the entire Napalm Death discography that is under 60 seconds long. Just throwing in related life advice for OP and any other commenters.

Perhaps you meant instrumental rather than jazz or take a rather wide interpretation of what jazz is. (another debate altogether).

Thing is that, for quiet/fancy restaurants, the music needs to be somewhat in the background. Enough to distract away from random noises but not so loud that it drowns out conversation.

The thing about music is that we (humans) are quite attuned to the sound of voice. We tend to zero in on the vocal line and the instrumental accompaniment is less prominent (although it can be "jazzy") So loud vocals and accompaniment are unlikely to be played in a restaurant.

For instrumentals, the instrument (or instruments) has to carry that "main" melody but few instruments can replace a voice. So the instrumentalist will have to introduce harmonies and variations that hold attention without being "cheesy". Imagine someone playing the piano that exactly mimics a vocal line and it'll very quickly sound like children's nursery rhyme music (not what most people want to hear in a fancy restaurant).

So the instruments get to play a more prominent and varied role and that perhaps sounds "jazzy".

You go to the wrong type of restaurant.
Most "fancy" restaurants play classical music or at least the ones I go to do.