There are other tools like Handbrake that are specialized for this task. However, Shotcut can do this task just as well. Here’s a thread of someone else in your exact situation along with a solution:
In your case, leave the width and height specified in the export preset so that all clips get forced to 1080. It might be necessary to separate landscape and portrait videos, and process them separately as 1920x1080 versus 1080x1920.