Consider adding single lights on either side of the mirror. If you happen to find something for 2 or 3, consider if the diameter of your shades will fit. Another consideration is the amount of light and shades might not provide enough. Is there a ceiling fixture?

https://www.anthropologie.com/en-ca/anthrohome/shop/lee-brass-fabric-shade-sconce-wall-light?utm_source=Pinterest&utm_medium=organic&epik=dj0yJnU9SFVMcS1uSTJzVDRoeTlVVlBnOGFncWxxYXFoUHlWeGUmcD0wJm49VFQ0VWdlTUJ6V2ZiN3c0WmxGMU5RdyZ0PUFBQUFBR29ZSUo4

Visit a lighting store and bring your shade with you. My search words was "vanity lights with fabric shades". Sometimes in the image you can see the wire cage like the image I posted. You can see the wire at the bottom of the shade. You need to purchase a light with the correct light bulb base that your shade will attached to. Some lights have chandelier bases and some medium or standard bases so consider what your shades attached to bulb wise. Often the glass shade can be removed as well and when using the right bulb you can use your shades. In your case I would visit a physical lighting store. You want to make sure you shade covers some of the lights workings and proportionally fits. It will be hard to do this online. Places like Wayfair has Specifications which is helpful but most times details that you need will be missing.

If you read/download the specs sheet and installation/assembly instructions for the wall sconces you are considering, it should give you that information.

Find the manufacturer webpage for all information that might not be shown on reseller sites.

I have two of these in my powder room and shades are the clip on type.

I would try Etsy, sellers tend to be responsive and help out - lots of lighting makers on there (i bought a bath vanity light on there)

Clip on can mean a lot of things. Do your shades have a spring wire that clasps to the actual bulb? If so you need to simply know the bulb style an size to know if your shades clip will fit the bulb. Downloading the spec sheet on fixtures will tell you the exact builb type they take.

Or do you have another type of clip?

The suggestion to visit a lighting store is an excellent one. There's nothing quite like having a sales or technical person have the item in hand for them to understand what you are looking for.

Thank you all so much for your responses! I hadn't thought of Etsy in terms of their responsiveness - that's a great idea! I don't live near any major lighting stores so I have to rely on online sources. To answer some of the other questions, the shades I have clip on to the top of the bulb like the picture below. Unfortunately the spec sheets haven't proved to be helpful because while they may take the same type of bulb it doesn't specify whether the lampshade clips on to the bulb or has a kind of cross bar that rests on the bottom of the fixture that the lightbulb sits on top of. Thanks again for all of your help!

I wouldn't think it would matter if the existing shade clips over the bulb or has the crossbar. Once you take it off, your shade should just clip over the bulb. The cross bar is usually attached to the shade, not the light fixture. Are you looking for a single sconce or a multiple light fixture for over the mirror?

It's easy to overlook something like that when you get down the rabbit hole of shopping for a certain item for a while. Good luck finding what you want!

What is so special about the shades you already own? Sometimes the juice is not worth the squeeze.

Big Box stores sell hardware fixtures w/o shades so you can create and individualized fixture, depending on what you mean by 'vanity light"....