I too have run into this in the last couple of months. First started when I was helping my FIL make a transition back to Outlook from Windows Mail which wasn't working right with certain types of mail formating (HTML code would be displayed rather than the actual message for some types of mail). Anyway, went round and round and eventually got an AOL customer support rep to fess up about the issue once I countered his response that no one's having any issues with my findings that there are countless forum threads citing this issue as far back as October 2022 or longer. He then changed his tune and said that one needs to stay logged in or repeatedly log into the AOL web mail for consecutive days then the App Password Generator feature will become available and work. Said they had issue with security of the App Password Generator concept and that they were working on a fix. Well duh, of course you will have a problem using an app generator because if your primary AOL login password gets compromised and as a result change your password, if the process doesn't wipe the app passwords, whose to say that a rogue actor hasn't already generated a new unique app password they can use in a third party client to still have access to your email. and then if changing your main AOL password were to wipe the App passwords then you need to go back and generate news ones for whatever third party apps you are using. But the interim work around to generate an app password is not publicly communicated by AOL and thus everyone is left scratching their heads. I know they are trying to protect us but sometimes more harm is being done than good and especially when a poorly thought out idea gets implemented then retracted with little to know disclosure.
Well, I took his advice and left my FIL logged in to his AOL web mail for 2-3 days and then the App Password Generator started working and I was able to generate a password and configure his Outlook client. But I'm not sure the days logged in is a hard and fast rule because I just recently created a new aol.com email address because of problems I'm having with delivery of text messages to my verizon.net email address sent from my Verizon cellphone and VZ's recommendation that the issue might be because of the legacy verizon.net email address that is now an AOL/Yahoo mail provider. Anyway, turns out I have the same problem with text deliveries using the newaol.com address but when I went to generate an App Password for my new aol.com email address and after about 4 days, am still unable to generate one. I won't even get into the debacle with AOL about the text delivery issues which I can't get a straight answer from either VZ or AOL as to whose problem is it.