Issues with lr and ps download

Is this what you paid for:

https://www.amazon.com/Adobe-Photography-Photoshop-Subscription-auto-renewal/dp/B07QZ9ZYKG.

Looks like Amazon did a piss poor marketing job, they use the wrong icon for LrC, and/or they do not differentiate Lr from LrC, but it appears to be the Photography plan.

Typically you subscribe to a plan at Adobe. When you do, you provide them with your e-mail account to use as an ID, and you create a password. Then you download and install the Adobe Creative Cloud Desktop App (ACCDA, aka Creative Cloud), that from:

https://www.adobe.com/creativecloud/desktop-app.html

You start ACCDA, you sign in, and then you pick from the available Apps, those you are paying for, and click on install. The ID you sign in with must be the same as at Adobe.

To check on what is in your plan you subscribed for bring up Adobe.com, sign in, and select to manage your account.

Back to ACCDA, when you sign in it checks with Adobe as to your subscription, It activates any installed apps (PS, Lr, LrC, Bridge, etc), if you sign out it deactivates them. It is used to (amongst others) authenticate your subscription, install apps, update/upgrade apps, activate apps, deactivate apps, install fonts, etc.

Now, if that Amazon purchase is legit, it should have interacted with Adobe servers to set up your plan, you might need to sign in at Adobe and manage your account, hopefully via an ID that Amazon passed along.