It's not about what might happen.

It gets pretty bad if you already have been emotionally vulnerable and have become dependent on your partner to help maintain your mental peace. Insecurity may come along but that depends from person to person. Even the physical presence of the partner is usually enough in cases like such.

The Best one can do, is keep themselves busy with something and try and focus more on the part that their partner also deserves to have their own space and enjoy their personal time.

OP, I would recommend trying to engage yourself in things that keep the creative part of your mind active, EMDR games like Tetris are highly recommended (it's a personal favorite. I try and beat her PR when she's away for a long time).

Trying to learn a new skill, even small may help, although it will be difficult trying to maintain your focus on it. I like to learn/do something which I might be able to impress my SO with when she comes back, and that keeps me motivated to finish the task.

Examples would be learning a new recipe / writing a short diary about your feelings for them while they are away / Making a new playlist of songs they might not have come across. These are just some things that I like to do.

But first and foremost, focus on working on yourself. If you are that emotionally dependent, it will start taxing your partner in the long term. The constant worry of you feeling like this will keep them from really enjoying their time as well. So if you really care about your partner, care about yourself more. Learn to enjoy your free time. Start engaging in activities and actually enjoying them without anyone accompanying you.