There is no automatic way to make a clip repeat itself after it has finished playing. If you set the asset length longer than the actual clip length it will only show the last frame as a still image.
In order to achieve the effect you want you would need to repeat the asset multiple times throughout the video so that when it finishes playing you have a new video asset that plays from the beginning to end again.
You will need some basic maths to work out how long the final video will be and how many times you will need to repeat the asset. Also if the final asset will need to be shorter in length.
If you don’t know the length of any of the assets, wither the overlay or the background asset you can use the probe endpoint and get the duration.
The probe endpoint looks like this: https://api.shotstack.io/v1/probe/https%3A%2F%2Fgithub.com%2Fshotstack%2Ftest-media%2Fraw%2Fmain%2Fcaptioning%2Fscott-ko.mp4
Where the url at the end is URL encoded and change v1 to stage as required.