How do I automatically add all existing apps to my home screen? When I got my first smart phone years ago, there was no app drawer. Every app I had was represented as one button in one app menu, so I didn't have to look in two places if I couldn't find an app. To me this was ideal, but now that I use Android phones I have to deal with both the app drawer and the home screen.

I just got a new Moto g7 Power (Android 9 "Pie") and backed it up from my old Android phone, so there are over a hundred apps on it. I want all of my apps to show up on the home screen so that there aren't apps lurking in the app drawer that I can just forget about, and so that the apps I want to use are easier to access. Is there any way I can automatically add all of my apps from the app drawer onto the home screen so that I don't have to manually hold and drag over a hundred apps one after another? It's fine if they don't automatically get sorted into folders etc. because I'm happy to do that myself.

When I looked up my question in the Play Store, I found an app called Smart Drawer but it's not even smart enough to know what a game is. Are there any other apps I should try?

It's maddening that it's so hard to find information about this. I would have expected this to be an extremely common thing for Android users to want to do.
Android launcher(s) is a dedicated app that serves as an UI to the underlying OS. There are tons of launchers available with features catering to the tastes of needs of users. If one needs features to be added to the existing (OEM or third party), they cannot be provided by yet another app because the launcher is so closely tied with the Android OS. Either the developer of the launcher, provides the requested feature or one uses a different launcher with that feature. 

Case in point is the requirement of OP to add all installed apps with the OEM Moto launcher (instead of having
 installed apps in the app drawer). OP is looking for the functionality of ABC launcher to be added to Moto launcher. This isn't possible for reasons explained.

Android users, usually, let pre and subsequently installed apps be in the app drawer and choose the apps, they access more frequently on home screen, organized in the manner of their choice. Launchers let you search for  apps, even when they are not on home screen. In the app drawer, they may be sorted alphabetically, or organized by functions (e.g.games) or user created panes (e.g. shopping /banking apps) etc. The possibilities are endless and there are launchers available for different needs. Nova launcher is famous for exactly this - letting the user customize practically each element of the launcher interface (the reason I use it)

tl:dr; You choose the launcher that works best for you