Axe progression works by improving Attack Speed, not Damage. A Stone axe does the same Damage as a Diamond one.
This pack makes it so that Axes scales through Damage and not Attack Speed.
Old Axes
Tier Damage Attack Speed
Wood 7 0.8
Stone 9 0.8
Iron 9 0.9
Diamond 9 1
Netherite 10 1

New Axes
Tier Damage Attack Speed
Wood 7 0.7
Stone 9 0.7
Iron 10.5 0.7
Diamond 12 0.7
Netherite 14 0.7

Gold Axes are irrelevent. OK
If you see the Axe's Attack Speed being 0.7, that means it is working. The Display Damage values can't change, or atleast I do not know how to do so reliably.