Because I did not know any better, I started by reverse-engineering how the Essential theme prints the header image as specified by that theme plugin's configuration setting named "logo".  That led me to theme_config::setting_file_url() in moodle/lib/output.lib.

That particular setting_file_url() function does not directly help me with my problem, because I want to get the URL of an image file that is specified by a configuration setting in a local plugin of mine.  But, it did give me other crumbs to follow:  the moodle_url::make_file_url() and ::make_pluginfile_url() functions in moodle/lib/weblib.php.

I then read the documentation in https://docs.moodle.org/dev/File_API.

I still cannot get what I want to work.  But, the above crumbs may help somebody.  I know that I have drifted away from the scope of the original post.