plan won't work

start here - https://helpx.adobe.com/manage-account/kb/stop-creative-cloud-trial-mode-after-purchase.html

if that fails, proceed to these steps - https://helpx.adobe.com/enterprise/kb/resolve-trial-and-license-expired-errors.html

if that fails, https://helpx.adobe.com/download-install/kb/adobe-license-issues-keychain-credential-mgr.html

if those all fail, change your cc language.  eg, try international english

if that fails, change the install location

Are you talking about Lightroom Classic (LrC icon) or Lightroom (Lr icon)?

What is the EXACT name of the plan that you bought? It should be on the e-mail receipt, and also if you go to account.adobe.com and log in, it should say what plan you have. Here is what my plan looks like at account.adobe.com, it says Photography plan (20GB)

When you installed the software, did you use the exact same e-mail address that you used when you purchased the software?

Hi, thanks for reaching out, and we're sorry about the trouble! 

I do see an active plan on your account. Try removing the Creative Cloud app completely and reinstalling it before trying to install Lightroom. You can uninstall the app using the Creative Cloud cleaner tool. Check the steps to use the Creative Cloud Cleaner tool here: https://adobe.ly/3F6NbBI