Knife project tool is looking rough after I extrude on a curved surface Hello Blender Stack Exchange Community!

I'm creating a cuff bracelet and using the knife project tool to "etch" text on the inside of the cuff, but the results are super rough.

The cuff (mesh circle) has a subdivision surface modifier (3) and the text is 2D (no extrusion) for reference. Any thoughts on what I might be doing wrong or how I could get a smoother etching effect?

Before knife project:


After knife project:
Apply an Edge Split modifier to your object and then select the loop edges one for each letter-symbol (if I count correctly there should be 5) and then once you select them press Spacebar and search mark sharp and press Enter

Then in your Edge Split modifier select only Sharp Edges.

However this will only fix the solution 90%. If you zoom in really close to the area with the letters you will see some "unwanted" shading. In that case I would suggest to delete the letters and try what comments suggest.