What is the secret to making widgets act like app shortcut icons do?

On all my computing devices, I strive to maintain a single-page
desktop/homescreen with _everything_ I need on it but always in
well-organized folder & menu hierarchies (impossible on iOS though).
<https://i.postimg.cc/7LmRqXNn/organize01.jpg> Android organization
<https://i.postimg.cc/bN7bp2Bf/organize02.jpg> Windows organization
<https://i.postimg.cc/LXzB3Lc0/appleid01.jpg> iOS (lack of) organization

One thing that has eluded me up until now are "widgets" which, for whatever
reason that I do _not_ yet understand, don't fit into folders where they
belong (alongside the normal icon shortcuts for app launches).

Up until today...
a. The widgets wouldn't go into folders - they had to be on the top
b. And they didn't usually take the form of a "normal" app icon
c. And you couldn't have more than one of them (in some cases)

All that changed today when I installed this app in testing for micky:
*Wifi Shortcuts+* by OpenGait.NET 3.8, 10K+ downloads, free, ad-free, etc.
<https://play.google.com/store/apps/details?id=net.opengait.wifishortcuts>

With Wi-Fi shortcuts I was able to create a widget that looked and acted
_exactly_ like app icons act in every way that I could imagine they would.
A. They had no problem fitting into folders and having multiple icons
B. They had no problem changing the background and foreground colors & name
C. They had no problem changing the icon itself just like with app icons

But yet they're widgets.
Huh?

What's _different_ about these widgets that they (finally) act like they
should in terms of being able to organize your homescreen how you like it?
--
Every day we all learn from each other because we're members of the team.