Can't open Photoshop Elements 2025 + multiple accounts

PSE is a 3 year term license, not a subscription.   You will find the download in your adobe product page.

One of the problems is probably the email address you are using to sign into Adobe with.   

Using what you are logged into this community right now go to your product page and tell us what you see.   

https://account.adobe.com/products

You should see something similar, dates are probably different. 

If you do not see something similar that probably means you are logged in with an email different than the one used to purchase pse 2025.

Beginning with pse 2025 there are two major changes:  No serial numbers to worry about, and your purchase  is tied to the email account used for the purchase, and the computer you used to purchase the product on. 
 

ABOUT THE TRIAL MESSAGE:  uninstall whatever version you get the trial message about if you can.   To do that first log out of the editor.   Uninstall the program any way you see fit-- I use Ccleaner for example.

Once you uninstall pse 2025, if you can, simply redownload it from your product page- it’s not part of the creative cloud family- no reason to even concern yourself with that right now.

When you go to download it:  an install file is first downloaded- run that, and the installation / download will happen automatically-- I seem to recall the initial download is about 4.3GB-- in order to keep the download relatively small components such as Adobe camera raw are downloaded automatically the first time you try to use them.