I notice that document does explicitly list GBU-39 as integrated on the B-2; pertinent to is it integrated/is current only planned to be integrated discussion.
Sure, but contra that:
GBU-39B Small Diameter Bomb Weapon System
The GBU-39B Small Diameter Bomb, or SDB, is an extended range all-weather, day or night 250-pound class, guided munition. The SDB relies on the Global Positioning System to provide navigation to thewww.af.mil
The F-15E Strike Eagle is currently the only aircraft outfitted with the SDB weapon system. Future platforms include the F-16 Fighting Falcon, F-117, B-1 Lancer, B-2 Spirit, F-22 Raptor and F-35 Lightning II.
Now, that's at least somewhat out of date (F-22 and F-35 have been cleared, I think), but it's not resounding endorsement of the idea that the B-2 can carry SDB-I.
And after some digging around on Twitter, I found a ref that sounds like he knows what he's talking about. (Usual caveats for Twitter reliability, etc. But poking at his blog, he mentions having worked on the B-2's Smart Bomb Rack and JDAM integration for the RLA, so I suspect he's legit.)
View: https://twitter.com/SMSgt_Mac/status/1511547774361341953
Depressing if true, and it sounds like something USAF would do.