Looks like a Lindera but that wouldn't be semi-evergreen. (right?)

Whatever kind of plant it is persisting foliage could be due to juvenility.

When I first glanced at it I thought it was dogwood but no. Could it be some kind of Rhamnus?

I dunno, but opposite leaves should narrow choices.

Many (if not all) Rhamnus have serrated leaf margins.

Is it opposite? I can’t really see clearly enough to determine.

It was hard to tell whether the branches were opposite. I found another pic on my phone but it's not definitive. Seems whorled in a lot of places.

Grey bark, white spots

Simple elliptical leaf

Entire leaf margin

Pinnate venation

(Looks like) one-bundle leaf scars

Branching habit reminds me a little of sassafras. It's not a Persea is it? (Not a genus that I'm familiar with at all)

Where's alabamatreehugger when we need him. Review his entire thread.

How about Symplocos tinctoria? The bark and Leaf shape are a good match, and it’s evergreen as well, but it also definitely has alternate leaf arrangement:

https://plants.ces.ncsu.edu/plants/symplocos-tinctoria/

This doesn’t look like a true evergreen to me. I think it’s as Embo said, just hanging on to leaves because it’s young.

I may have to wait until spring for more clues, maybe it'll be in flower. I saw multiple trees like this, and one was probably taller than 10 feet (First picture, but I just took one of its trunk) and all held a few leaves with some being purple. It's in a disjointed microclimate area that is more similar to the mountains/foothills than the piedmont. (Hemlock Bluffs Nature Preserve in Cary NC). They have a relic population of Hemlocks, and there is Galax, etc that are usually more common to the mountains. I'll try to remember to go back later and update this post.

The opposite leaf & stem arrangement is clearly seen in the 2nd pic down.

Trunk bark doesn't match Rhamnus in any of the above pictures.

Yes, I do see what looks like opposite arrangement but I also see ambiguous arrangement in other pictures. OP says it was hard to tell.

Be sure to visit the exhibit hall in the Stevens Nature Center. When you stop in, you can chat with staff...

When exiting the nature center, check out the beautiful courtyard gardens...

Hemlock Bluffs Nature Preserve - Friends of Hemlock Bluffs

Red Bay or Lobloly Bay? Zone 7b where?