Account Audit Functionality
What I'm suggesting is some functionality to allow you to audit what information each company has about you. Say you have a log in for your bank. They probably have quite a lot of accurate personal information about you, such as your full legal name, address, phone number, and a significant amount of financial information. Maybe they also have some sort of legal ID number for you too. If they are breached, you would want to know exactly what's at stake.
This could take the form of something super simple, like a checklist that identifies yes or no whether that company has that information, with a checkbox for specific information like name, address, DOB, etc, or for whole classes of information, like employment information, employment history, health information, demographic information, special category data etc. Then, if they're breached, you can quickly identify what sorts of information they held on you. Currently, I do this by making a note in the description of my Pass entry for that site.
I also use this to highlight password limits or requirements of sites and MFA limits. For example, I would want my passwords to all be a minimum of 24 characters and be able to have special characters and numbers etc. Then if I audit my passwords I can quickly see which ones don't conform. However, some of these don't conform because the service does not allow these passwords. I make a note of that so I can check in the future whether they have improved and I can bring my password up to standard. Similarly, when I can't put MFA on an account, or if I only have the option for email or SMS MFA, I note this down so I can follow up in the future, and not wonder why I never put MFA on that account.
Taking that a step further, maybe you could have specific fields for name, DOB etc. This would be particularly helpful if you use different names or different permutations of names for different services. Perhaps some services (like your bank) have your full legal name including middle names. Other services perhaps have a first initial and last name, or a first name and last initial. Maybe you have a pseudonym you use on other services. With specific text box fields for individual types of information, you can identify not only that a company holds your name, but what form that takes. This has the added cobenefit for those who are changing their phone number, address or name as they can quickly see who they need to update.
I think this has a lot of potential in terms of privacy, breach management and scam avoidance, but also ease of life for big transition moments. I think it could also slot in really well with improvements others have suggested in terms of breach monitoring and dark web scanning for login information, prompting you to go look at what companies hold, or, if we were getting really fancy, identifying what types of information were breached (for example, haveibeenpwned notes what types of information were obtained in a breach, so this could be highlighted in the login entry.