I've purchased the app in Nov 2019 and used only on mobile.

I tried to install on my laptop.
I went my Google play store and it shows "Install on more devices" but when I click it, it doesn't recognize the laptop that I am accessing the site.

What should I do?

You need to get the app from the Microsoft store if you want to install it on Windows.
The Android app that you see on the Google Play Store doesn't run on Windows