Did my best to check things for you. Via myphpadmin for the database.
For the "information_schema" for the databases, under COLLATION_CHARACTER_SET_APPLICABILITY I clicked the "Structure" tab and I see:
COLLATION_NAME and CHARACTER_SET_NAME are both type: varchar(64) and Collation: utf8_general_ci
Then looking at the list of many possible Charsets for the database and scrolling down to utf8_general_ci, I see:
Unicode, case-insensitive (this Charset is also shown to be the default).
I found the table "plugin_storage" and filtered rows by searching for "favorites" and there was one line. I clicked "Copy" so I could see it, I found a list of one favorite. Apparently, in my original post I forgot to mention that on the fresh install, when I turned on the favoritesHandler plugin, the site did not throw the error until I (who was logged in as the admin) clicked "add to favorite" for a picture to test it. As soon as I clicked "add to favorite", the 500 error appeared, and did so every time I turned on the plugin when logged into the site on the front end (thus it does not throw the error if I open an incognito tab and am thus not logged in, until I log in, even with someone else's username than my own, for which there would be no favorites saved yet). My apologies for not having noted this earlier... it happened so fast, and then I tried to trouble shoot for a while before posting.
Because of this one-time clicking of an add to favorites before the 500 error, there are four sections of data:
for: id int unsigned, there is nothing (Value box is blank)
for :type varchar(32) the value is "favorites"
for aux varchar(255), there is "David"
for data longtext, there is my entry:
a:2:{s:4:"type";s:6:"images";s:2:"id";s:55:"Christmases/Christmas-1975-79/DavidKidChristmasTree.jpg";}
If you need anything else, please let me know, and thank you so much for your help. Sorry again I didn't mention that the site didn't throw the 500 error until the first time I clicked "Add to favorite" before. I didn't even think the favorite was saved, as the error was instant, if I remember correctly.