Due to the fact that a global was used on GenerateSpecifiedFilename to
save the remux file name, when a screenshot was made, it would overwrite
the filename being remuxed, because screenshots use the same function to
generate filenames as well.

This solves that problem by removing the global and the changes to
GeneratedSpecifiedFilename, and isolating that to the output handler.

Coincidentally, this bug probably also happened with replay buffers
under certain circumstances.

Fixes obsproject/obs-studio#3497
Closes obsproject/obs-studio#3498