As of late 2023, the last time I checked this, the only PvP titles that are account wide are generic ones such as Conqueror, Battlemaster, Bloodthirsty and Khan ect, as they have always been. Any ranked titles (Arena/RBG’s) are character specific, unless they changed something TWW, but I feel fairly confident they did not.
Character specific titles also apply Legacy Ranked titles from the original PvP system in Vanilla which I have on my shaman and warlock.
Edit: A quick search seems to confirm this, here’s a thread from the same period of time.
Edit 2:
MODERN WOW
Arena titles are granted immediately as soon as you reach the necessary rating and once earned, the title lasts until the end of the current season. You can keep track of the titles you had in the past by looking at your Feats of Strength.
Rated Battleground titles are permanent.
PvP titles are not account wide and can only be used by the character that earned the title. This includes the Gladiator title: even if the Gladiator mount is account-wide, the title is not.
It would appear I must have earned it in 2014 as my achievement says. 20 years of this game makes it hard to recall the specifics all the time, but either way, something must be bugged with the vendor and my achievements.