You really do not stain gluelam. The clue to that is in the word Glue. Glue doesn't take stain, and trying to stain it will just make it look splotchy and ugly.

Thank you @Monique! I have a left over piece and was going to experiment on it. What is the typical treatment then? Or just clean up the pencil marks and leave it as-is?

I feel like it's distracting attention from the fireplace. I'd paint it to match the ceiling.

IMO you will need to cover it with some actual wood if stain is the plan and then IMO it will depend on the wood you use you could match the floors or the mantel either will work or drywall and apint to make it not a feature.

"You really do not stain gluelam. The clue to that is in the word Glue. Glue doesn't take stain, and trying to stain it will just make it look splotchy and ugly."

There is no glue on the surface of the beam to inhibit stain absorption with the exception of the lamination lines which are microscopic. Staining the knots could be problematic.

Drywall and paint same color as ceiling.