How do I modify an organization contact only for myself?

I want to associate a nickname with a person in my organization, whose employee records live in Entra ID. To do this, I went into Outlook desktop (1.2024.1204.300), did a search for the person, and selected "Add to contacts". From there, I modified the newly created contact record's first name from, for example, "Margaret" to "Margaret (Peggy)". I also deleted the company and title fields that got auto-populated because I don't want to overwrite these values from whatever they might change to in the future. The only fields I should need are email address (which I expect it needs as the "key" to match my contact record to the person's underlying record in the organization) and the fields I want to overwrite, in this case first name. From here, I'd expect interactions with this user to show their updated name for me. It doesn't.

Nothing works as expected. If I start a new email and type "peggy" into the "To" field, nothing comes up. If I type "margaret", she appears in the results without my name modification. Similarly, while in the Mail section of Outlook, if I do a search for "peggy", I get no results, even if I filter on People. However, in the People section of Outlook, if I do a search for "peggy", she does come up. So even within Outlook itself, there's a total disconnect between how Mail and People honor my contacts info.

In Teams desktop (24295.605.3225.8804.), it's even worse, with there being no trace whatsoever of the contact's updated name. In the People section, "All contacts" shows nothing at all.

I've manually clicked Mail > View > Sync in Outlook. I've tried manually closing both Outlook and Teams. I've waited 30 minutes. I've even confirmed via outlook.office.com that my contact is there and that the "new contacts" settings is on, but actually seeing the updated name when writing an email or sending a Teams chat isn't working at all. None of these time-consuming and frustrating steps should be necessary to begin with, but even then, it's all broken.

Is this not a supported feature in M365?