I would go with nice chandelier.

Yes chandelier, if you can move the electric to the center of the ceiling, not on a beam, I think that would be great!

and maybe wrap the beams with wood.

Do you need a fan? Where are you located?

No ceiling fan light or torchiere floor lamp. Use table & floor lamps plus accent lights for art, special architectural features and as uplights under plants. I would look for a mix of lamps that echo the era of the settee and chair plus something more modern to continue your eclectic style.

You have a variety of options here. You could replace the fan with a chandelier, you could use sconces on a wall, or you could also just use lamps. Below are some of our designs that show you your lighting options.

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Do you need a fan? There are many fans that are nicer than the one that is there. You can also do one with out the light and do other kinds of lighting in the room. Or do one of the combo units that looks more like a pretty fixture...

Good luck

Definitely do not wrap the beams in wood.

I would replace with a period light (as well as have lamps and other ambient lighting).

You can find authentic ones or reproductions. I would not put a sleek, modern light or fan in this room.

Examples:

https://www.rejuvenation.com/catalog/products/wildwood-semi-flush-mount?cm_ven=PLA&cm_cat=Google&cm_pla=default&cm_ite=A4860&gclid=EAIaIQobChMI6qfIsKbL8wIVCWpvBB1ezABmEAQYASABEgKZ6_D_BwE

https://www.build.com/product/summary/1460312?uid=3437038&jmtest=gg-gbav2_3437038&inv=1&&source=gg-gba-pla_3437038!c1710655145!a67979306878!dc!ng&gclid=EAIaIQobChMI_Of1rKjL8wIVBmxvBB229gPsEAQYAiABEgLl7fD_BwE&gclsrc=aw.ds

https://www.build.com/product/summary/778551?uid=2008151&jmtest=gg-gbav2_2008151&inv=1&&source=gg-gba-pla_2008151!c1710655145!a67979306878!dc!ng&gclid=EAIaIQobChMI_Of1rKjL8wIVBmxvBB229gPsEAkYAyABEgJHCPD_BwE&gclsrc=aw.ds

A few things for fun:

This next gorgeous light is in this 1910 house: https://www.oregonlive.com/life-and-culture/j66j-2020/03/59e87d16f11434/the-mysterious-1910-emma-austin-stone-house-in-lake-oswego-is-for-sale-at-14-million.html

1910 Sears catalog lights:

https://www.oldhouseonline.com/interiors-and-decor/lighting-1910-to-1930/

http://www.vintagelights.com/category/vintage-ceiling-light-fixtures-antique/year/1885-1910-antique-lighting-fixtures-vintage-lights.html