I don't know what the + in front of the __FILE__ is supposed to do

In the current form, it has no meaning. It is a leftover from an earlier version, which read something like:

$MyApp::once{+__LINE__} ....
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and so the + stayed there and when posting my problem, I copied it without much thinking. If you have only __LINE__ as key, the + is needed because __LINE__ is a bareword.