The Poison Weapon feat grants additional benefits
The feat has different, more restrictive, rules because it also grants significant benefits.
A rogue does not have to use the Poison Weapon feat in order to apply poison to a weapon. The feat lets a character do so in a more action-efficient way. They spend one action to both retrieve and then also apply ...
I agree the rules are confusing. This is what I think makes the most sense:
A successful strike removes the poison from the weapon.
A critically failed strike removes the poison from the weapon.
Otherwise the poison lasts until it expires (if applicable to that poison).
If the poison was applied with the Poison Weapon feat, the following additional rule ...