I'm not a fan of shiplap so I'll give you a "bump" so others can weigh in. :-) The mantle on your inspiration photo is nice. Can't tell what kind of fireplace you have. If gas, make sure you know height and wall projection requirements for the mantel. Your fireplace looks higher than the inspiration pic so the mantel will be higher and depending on wall projection, might need to be a lot higher.

I don’t think shiplap idea would work in your case. First of all you can’t have combustible material near the firebox and if you place a thick mantle then shiplap over it then visually it may not look nice because there will not be enough room left between the ceiling and the mantle. Besides that, there’s not enough wall space on either side of the fire box. I would suggest to go with tile or wood look tile all around the fire box and take it to the ceiling for a seamless look.

You can also do a herringbone tile all over the fireplace wall