I was playing yesterday with this guy and he applied the Seppuku buff on both his weapons (as you can see - dual Falchion I think).
How? I am dual wielding 2 spears and both have the Seppuku Ash of War on them.
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You should be able to do this by two-handing your off-hand spear, using the Seppuku ability, then returning to using both weapons (or two-handing your main-hand spear), and using the Seppuku ability a second time.
This should apply the buff to both weapons.
To two-hand a weapon, you need to hold down the event-action button (Triangle on PS5, Y on XBox) and press the corresponding armament attack button for the left or right armament you wish to wield with two hands (R1/RB for right hand, L1/LB for left hand). You can then utilize the Ash of War that's currently equipped for the weapon you're two-handing.
For a visual example of someone applying the Seppuku buff to both their off- and main-hand weapons, you can watch the first few seconds of the following video by THE GAMER EYES: