Where is my album

That (your screenshot of iTunes preferences) normally means you do not have an iCloud Music Library (for the Apple ID being used to sign in). Do you subscribe to iTunes Match or Apple Music? Those paid services (having one or both) is what provides the iCloud Music Library. Otherwise, you don't have one. Maybe your wife's Apple ID has an iCloud Music Library, but the one you are currently using on the Mac does not.

In iTunes, click your name at the top of the window and select Account Info. On the Account Information screen, under iTunes in the Cloud, click Manage Devices. A list of devices currently associated with your Apple ID is shown. Is your Mac AND iPhone on the list?

You can also check there (on your Account Information screen) if you have iTunes Match and/or Apple Music, if you are not sure. The iTunes Match subscription is shown under iTunes in the Cloud. The Apple Music subscription is shown under Settings -> Subscriptions -> Manage.

Even if you don't have an iCloud Music Library, IF you are signed in on your Mac and iPhone using the same Apple ID, you can download past purchases (made with that same Apple ID) on the Mac or iPhone. This document explains how to do it.

Download your past purchases - Apple Support

No option for Manage Devices under iTunes in the Cloud.

That may mean you do not have any devices currently associated with your Apple ID. That may seem strange, since you are signed in on that Mac, but I believe you need to use the Authorize This Computer command under Store in the iTunes menu bar. Exit out of that screen, then from the menu bar, under Store, select Authorize This Computer. Enter your currentApple ID and password, to authorize your Mac for that Apple ID (a computer can be authorized with more than one Apple ID or none at all). Go back to the Account Information screen to see if your Mac now appears as an associated device.

Now, why doesn't your iPhone appear as an associated device? If your iPhone does not appear there, that may mean you are actually not using the same Apple ID on your iPhone. You mentioned that you were using your wife's Apple ID on iPhone previously. On the iPhone screen, open Settings and check iCloud. That should be your Apple ID there. And also tap iTunes & App Store; make sure you are signed in using your Apple ID there.