To recap, the problem arose because the xindy_lisp.exe executable invoked by the xindy.pl script cannot cope with Umlauts (or presumably, other special characters) in file and directory names. This post a problem for me, since my username is "Jürgen" and thus many of my files and applications are located in my "C:\Users\Jürgen" folder
Furthermore, even after I removed both my MiKTeX installation and my test .tex file from the "C:\Users\Jürgen" file, the problem persisted. After following advice I had received here, I examined my environmental variables and discovered that both the HOMEPATH and LOCALAPPDATA made use of "\Users\Jürgen", and that xindy_lisp.exe somehow tried and failed to access either or both of these directories (even though there was nothing relevant there).
Thus, I needed to change these environmental variables. However, since I don't know what other software made use of these variables, I wanted the original directories to remain accessible. Thus, I decided to set a hard symbolic link. In the Windows Terminal:
mklink /J C:\User_Juergen C:\Users\Jürgen
This had the added benefit of making the .tex files in my Google Drive accessible to xindy-lisp.exe, since my Google Drive folder was also within my C:\Users\Jürgen hierarchy.
Thus, I set HOMEPATH="\User_Juergen" and LOCALAPPDATA="C:\User_Juergen\AppData\Local", and xindy-lisp.exe ceased to cause a problem.
Thanks to everyone who helped me figure this out!