I've dealt a lot with security-related ordinances. Most cities don't have them, but they're gaining in popularity.
If you're worried about break-in's, an applied film won't do much. Statistically, burglars don't break glass unless they have to. There are very quiet ways to get doors open that attract less attention.
A "charlie bar" is the very best way to make it hard for someone to break into your house using your storm door. Many security ordinances require them, and they are easy for anyone to install.
The glass in your door is tempered glass
, and honestly it would take a baseball bat to break it (or a very small sharp object like a nail set or screwdriver). You can't retrofit it with glass that is stronger. It is tempered because of the risk of deep lacerations if you fall into non-tempered glass. Tempering makes it much harder to break, and makes it break into very small pieces if it does break. Your average window is not tempered, and can easily be broken with any object or a gloved hand.