Appian as the backend for our external application

Yes you can. Not sure what you mean with "login". When using APIs only, you would use service accounts for communication.

IMHO using Appian as a headless backend is not a great idea. Appian is meant to implement business processes with human interaction. For that interaction you design interfaces in Appian and make use of the built-in process and task management capabilities. In your situation, you would probably lose all these benefits and end up reinventing the wheel. But that's just my opinion without knowing any details about your use case.

My question is whether there are built-in APIs to take advantage of full user management functionality for our online applications or if we need to create our own user management within the Appian platform. In my case, there are two sites: one on our local servers for administration purposes and other internal business process management, and the other is an online website that helps our partner login and use some online services. Our admin who works on the local site will define the users for the first time, and when our partners access the portal, they will proceed with the password change process and login in the same way as done for Appian local users.

There are no built-in APIs for user management. But you can easily create some web API endpoints in Appian to expose the functionality you need.

Did you consider SSO and an external identity provider?

In our current application, there is no single sign-on (SSO) functionality; therefore, the requirement necessitates a login page for our partner, which will require a username and password. As you are aware, we cannot expose our Appian application directly; consequently, we have developed a customized front-end application for online use. It is imperative that the same login functionality and password policy implemented on the local Appian site be applied to the online version as well.

Do you have any recommendations regarding our aforementioned request?

Not really. I do not see any Appian certifications for your account. But I assume you have enough Appian expertise in your team to develop the necessary processes and expose them through APIs. For creating the users, you might have to use a plugin to be able to define the passwords yourself.

To clarify my request, we are currently in the analysis phase prior to engaging in detailed technical tasks. I would like to ascertain whether I possess the capability to reset or change an Appian user password from an external application via API.??

Yes, you can reset or change an Appian user password from an external application via API.

I am not sure I understand your question. Using smart services is the only way to manage user accounts in Appian.