The widget type you describe is what’s referred to as a “legacy” widget. Back in iOS 8 (2014, I think), Apple introduced the concept of widgets, giving us the ability to add windows of glanceable data from our apps. These widgets were interactive, meaning that you could control the app within the widget itself. These widgets could only be added to the Today screen — this is the screen that you can see when you swipe right from the lock/home screen.

As of iOS 14 (in 2020), Apple redesigned the widget framework and allowed us to place widgets pretty much anywhere in the Home Screen as well as the Today Screen. Different from the “legacy” widgets I described above, these widgets only allow us to view data, without the ability to let us control the app itself. Tapping one of these widgets can usually only allow us to open the app itself.

It turns out that Apple has allowed the “legacy” widgets and the iOS 14 widgets to co-exist; as you mentioned, your app’s widget can still only be accessed from the Today screen, at the very bottom, to boot. I keep waiting for Apple to decree “legacy widgets will be deprecated as of iOS NN” but they haven’t done it in the last 2 years, so perhaps those old widgets are here to stay.

I’m not familiar with your app, but I’m guessing that the developers believe that their legacy widget is more functional than converting to the iOS 14 style widgets. Either that, or they haven’t bothered to do the necessary work to build the newer-style widgets. You may want to contact them and ask, or simply request that they develop a newer-style widget for their app.