HI -- I don't think staining the frame the same as the vanity is the thing to do ... too dark . I would paint it a color that will go with the counter top like a creamy white , in a high gloss .

I think it might look better if you turn your mirror 90 degrees so that it is vertical versus horizontal. Be sure to hang it 4-5 inches above the vanity top. It doesn't need to be the same width as the vanity top. Lefty's right-paint it instead.

I think it looks perfect as is? The contrast in woods is very nice and the mirror is actually useful as is vs vertically. Make the room look bigger. I have framed many a mirror in CA as full with vanity mirrors were very popular but become dated without the addition of the frame.

Try staining a lighter color stain vs the java color.