some of those anatomical bends are really tough to get into some stems.

I'd estimate if it's quill style, there's 99.1% chance it's a 1" stem. Seems to gybe with your measurement. I think the standard stem diameter for a 1" is 7/8", but 13/16 is pretty darn close to that.

Hopefully your stem isn't a 25.4 bar clamp.

Hopefully your "new" bar isn't a NOS pre-1998 Cinelli.

What else can you tell us about the bike, stem, old bar and new bar?