Perks that are managed by the PerksQuest quest do not remove their effects on the game if the perk is lost (such as by making a skill legendary, or spending a dragon soul in apocrypha) because there is no script that undoes their change. Likely because there was no legendary skills in 2011.
This effects the perks Persuasion, treasure hunter, golden touch, master of the mind (but only in a way that doesn't do anything in the base game), and master trader, allowing you to keep their perk effects post legendary skill. A similar bug noted on UESP also effects the investor perk, so this is a bug with all perks managed by quests, not just ones managed by the PerksQuest specifically.
You can verify the bug by checking a (reset inventory) merchant's gold total before and after legendarying the skill, or by passing a persuasion check with a difficulty known to be too high to pass, such as talking your way into the college of winterhold with only 70 speech. In fact, with persuasion in particular if you get the perk and reset it repeatedly, then legendary the skill you can continuously lower the difficulty of all speech checks until a 15 speech can pass all checks
I have been able to replicate this bug with an empty load order and a load order empty save the unofficial patch. It can be fixed by not using the PerksQuest to change globals, instead tying the global changes to an ability with a magic effect that makes the changes when it starts and undoes the changes if it finishes.
Issue Data
Issue #35677: Perks Managed by PerksQuest (Persuasion, ect, Golden Touch) Still effect game when perks reset