It's all explained here. Anyone can do a confirmed change or standby via the app but there are some limitations...

• There is a fee between $75 and $150 for confirmed changes, unless you are in a premium cabin or are OWE. That's a pure revenue grab and AA does it because they can.
• There are a limited number of seats available for confirmed changes. The exact algorithm is murky, and the app and the website sometimes give you different availability. No idea what's behind this. You just have to embrace the mystery.
• If you've been upgraded to domestic first class you can then do a confirmed change into first class on any other eligible flight that day.
• Anyone can stand by for an earlier flight. Only elites can stand by for a later flight. One assumes this is because non-elites are less likely to clear the standby list and would risk being stuck. AA is just avoiding a potential customer service headache here.
• No changes to origin or destination or connection point. This is an IT limitation and lets AA make the change without a ticket reissue. DL and other airlines have more flexible systems.

The above rules govern the automated changes through the app and website. Generally if you approach a gate before boarding and ask to go standby they will put you on the list if you haven't checked luggage.