Changes remain after uninstalling

Please check whether the file extension setting in “functions.php” file in the theme folder exits or not.

Basically, WordPress permits uploading some file extensions. This plugin can add to allow uploading specific additional file extensions and avoid to sanitize a file name while the plugin is enabling.
In other words, after the plugin deactivates or uninstall, WordPress behaviors to allow some file extensions and to sanitize a filename by WordPress standard policy.
So, I recommend that you install new WordPress as the demo, and try to check the behavior.

You are right, I had the function allowing those file types in my functions.php file, but my goal was to use that function and not your plugin.

The main issue is that uploading these files now adds this random string to the end of the file name. That did not happen before installing your plugin and what I want to remove. What would cause that?

If it is sanitized by wp_uique_filename function, I think that another plugin or code in functions.php (using wp_check_filetype_and_ext hook) may be sanitizing the filename.
Firstly, I recommend that you confirm whether the issue occurs or not by changing the theme to default theme which functions.php aren’t customize. If the issue occurs, you confirm whether the issue occurs or not by disabling all plugins.

It turns out this is an optional feature within WooCommerce settings. I didn’t enable this setting and this wasn’t happening before installing your plugin, so it seemed like there was a connection. Perhaps I updated WooCommerce in the interim which enabled this feature. I’m not sure how else this could have been enabled.

Regardless, thanks for your help.