I originally got this game to help me learn and maintain my skills with German as I heard the German version of this is fun. After I booted the game up however, I noticed there was no language selection in the options menu nor any flags on the main menu; so how do I change the language?

You need to download the German version, there is a separate installer.

I don't see this on my account. And my version (English) doesn't have an option in-game to change the language. Has the German version been pulled?

I bet German audio with English subtitles would be good!

nope. See screenshot. I also just tried the download, works flawlessly. You should be able to create that on your own.
Install and backup both versions, then copy the audio from one over the other. It's all separated wave or ogg files, so that should not be much of a problem.

Thanks for the tips, neumi5694! I didn't know Gog's download page functioned that way. (From the past, on other games' pages, I vaguely remember seeing non-English language editions posted together with English on the same page, without that dropdown interface.)

That is the case if one installer contains multiple versions (Simon the Sorcerer for example) or the game is multilingual.