Here's the solution. It's obvious but not that obvious 😝
Basically, when you've installed WhatsApp, go to settings and grant Storage & Media permissions. Then, and Only then, open WhatsApp, enter your number and boom, you'll get the pop up that a backup has been found. You don't need to install an older WhatsApp to do this. Install the latest one and just remember to enable that permission before you enter your number. Hope this helped