Can this closet header be removed?
You really need someone to look at this in person, not through an internet straw. Some notes that may help...

Builders almost never use 2x10 for non-load-bearing headers. They're expensive and it's wasteful. That doesn't prove anything here, though.
The drawing shows the primary bearing wall being at the back of that closet. That doesn't prove anything, though.
You don't report seeing or hearing settling when you removed the header support studs. That doesn't prove anything, though.
You could investigate the headers over the adjacent hallway and along that plane to see if they're load-bearing. That doesn't prove anything, though.
You can examine the lower level to see where loads are transferred through the basement walls or posts to the footings in the foundation. That doesn't prove anything, though.

It's the accumulation and analysis of such clues in aggregate that leads to a reasonable and safe conclusion. We can't do that from here without a protracted and cumbersome conversation. That's not really what this site is for.
Good luck.