You can either get new lighting with a longer arm, or if it is only an inch, put a 1" piece of wood between the wall and the base of the light. If you use a round piece the same size as the base, and paint it in your wall color, I don't think you'd notice it since it's in an alcove.

I can't clearly see your crown (or cove?) trim profile, but what about a wood mounting box in the same style to go over the cover the electrical cut out, and allow the sconce to extend the proper distance? It can be painted the same as the wall color or the trim color. Might need it custom milled, but it's doable.

ETA - on second thought, maybe do round with a routed edge.

@calidesign, we must have been writing at the exact same time - lol!

So these Library Swing Arm lights are available with arms in various lengths. This is just quick paste up to illustrate you require longer arms. This is not exact.!!!

I'm sure that there is one that will fit the size needed. I have no idea how much you wish to spend so I have included a few sources but there are scores of these lights out there.

https://www.lampsplus.com/products/robert-abbey-alloy-warm-brass-plug-in-swing-arm-wall-lamp__42e35.html

https://www.lumens.com/aidan-swing-arm-wall-sconce-by-norwell-lighting-R360610.html?utm_source=google&utm_medium=PLA&utm_term=&utm_brand=Norwell-Lighting&utm_id=R360610&utm_campaign=1440416580&gclid=Cj0KCQiAv6yCBhCLARIsABqJTjYorjFRRplKgUZF01Lom0hHpi5zbgS9IO8dsr4XlLirQB8RTk4p84oaAokWEALw_wcB

Please note that your light shade needs to be out quite a bit in front of shelves so you get a nice spread of light and not just a hot spot on your built-ins.

You could use an electrical box extension ring. You'd attach the ring to the electrical box in the wall and then attach the light to the extension ring. Yeah, it's not beautiful and is generally installed inside a wall but given it's location (tucked back above a bookcase), if you just painted it white it would probably be okay.

If you’re going to get a new fixture, and want time to think about it, could you just face the current lights up towards the ceiling as a short term solution? It should give you a low light/ reflected light look that might be ok.

Is the rectangular box in the ceiling in front of the bookcase an electrical box? Is it centered on the bookshelf side-to-side?

BeverlyFLADeziner I didn’t know they had so many sizes. The lighting company we used only had this one light. Thank you so much!

Thank you to everyone else that replied. I appreciate your help and suggestions.