Even centralized logs can have rotation and retention.
The company will have to decide for themselves, primarly, if some interest is legitimate.
This means you weigh the data you collect by the single user against the continued function of the company, the great good and all other users. The company should then be able to demonstrate this process to the regulatory body.
There is no nailed process but keeping logs for a short amount of time to ensure network security and keeping some logs longer for legal compliance will most certainly pass as legitimate interest.
Network security benefits the user themself, the company and all other users by ensuring their data is secured against breaches. It goes beyond simple self-interest of the company and protects the users too.
Similarly having an email address to contact a user can be legitimate interest. If you only send them informative mail, ie "Someone changed your password" and "We had a databreach" or even "Someone tried to login from Uganda using your password, check if that's alright please" it serves primarly to protect you, the customer and the relationship you build up.
IMO that means it's legitimate.
On the other hand, of course an adcorp could claim their personal tracking data is legitimate. The data collected does not benefit the user other than showing them ads and selling it to others. Of the three groups, only one benefits.
Or keeping a webserver log for 20 years including usernames and emails.
IMO that would mean it's not legitimate.
If you are wrong in what you think is legitimate, you get a sternly worded letter from your favorite regulatory body asking you to fix it.
If you think they are wrong about that, the best option is to write them back and explain why you think it's legitimate. You can work out a solution with them that satisfies both sides.