Lightroom subscription problem

Ah, dj_paige has a excelant point. And relooking at your screen capture, seeing a Lr shortcut, not a LrC shortcut, makes me wonder. Lightroom Subscription, or old Standalone Lr. And Lr cloudy vs Lightroom Classic.

I see the icon has the rounded corners not square, so probably Lightroom Ecosystem (Cloudy)

I have already purchased Lightroom but when I installed it on my mac computer it wanted me to pay. How can I fix this problem?

By @Mike3228767337r9

What is the EXACT name of the Lightroom plan you purchased? Please be specific and exact. Please go to account.adobe.com and look at the plan you have purchased, mine looks like this, I have purchased the Photography Plan (20GB).

What is the exact name of the software that you actually installed? Please be specific.

@Mike3228767337r9 confirm you are logged in with the correct account email. Try logging out and back in.

Check your account status through the Creative Cloud desktop app.