Dark Val doesn't have a bat.
Of course not, original-Val has the "antique" bat.
Mender presented it to her. That's what I'm referring to.
And if its Mr. Bat 74 rather than Mr. Bat 2, it still raises questions. Is baseball still a "thing", 200 years from now? Why wood? Why not some more exotic (and superhero-appropriate) material, obtained during Val's "missing years"?
Mr. Bat is something that would be very significant to Val, and it was just a last-panel throwaway line.

HYPOTHETICAL dialog (need to shoehorn in an extra panel or two somewhere to make it fit...):
Mender: We got Mr. Bat out of storage for you.
Val: Why is it completely black?
Mender: It was carved out of meteoric basalt during the invasion of....never mind...
HYPOTHETICAL #2
Mender: Here's Mr. Bat.
Val: Not the one I remember. What is this made of, and why is it patterned like that?!
Mender: Nanotube carbon-fiber. Unbreakable, but flexes with recoil just like wood...
Val (grinning): I think I'm gonna like this...
Hypothetical #3:
Mender: Here's Mr. Bat. We borrowed it from the museum.
Val: Will that be OK?
Mender: Sure, it's unbreakable. We just have to put it back when we're done.
Val: Its....its....transparent!
Mender: Crystallized titanium alloy.
Its really a shame that Val's (likely) reaction to being handed "her" weapon had to be glossed over due to the narrative form. There's only so much "she just rolls with the strangeness" that suspension of disbelief can cover.
That's a conversation that could have taken up a whole strip, and it was too soon; she really didn't need a weapon just then, in the peaceful confines of the Temple of Light.
Hmm, I know what's done is done, but preface each hypothetical with Val saying "I need a weapon," maybe insert a page between Another World XI and Another World XV, man that would have worked so well...