Firstly, I googled "Active Directoy Password Authentication" as I have never heard of it. Nothing came up, but what did come up is:
"Azure Active Directoy Password Authentication"
So, are these typos? I am going to run under the assumption that they are and explain them all:
Windows authetication - this works because the account you are logged into the machine as has access.
SQL authentication - This is very common misconception. Because you are asked to provide a username and password, most people think they can type in their Windows accounts here, but it is not how it works. SQL has it's own INTERNAL user database, and when you use SQL auth, it looks for the user in SQL itself, not AD. You won't have any users created in there yet. As an example, have a look around in SQL Studio for "users", you will then be able to create a an SQL "user" there. It is this user you must userin when using this type of auth. Windows or AD account WILL NOT WORK.
Azure Active Directoy Password Authentication - Azure AD is not the same as normal AD. It has it's own AD users (which is not the same as the ones you have on your local AD). MIcrosoft is in the process of renaming "Azure AD" to Azure Entra" because of all the confusion it causes by people thinking it is the same as a local AD, it is not.
Same goes for the other methods which I assume all have Azure in front of them (from what I read on the net just now)