Curry, 57 bytes

This being my first Curry answer, I'm pretty certain its not quite optimal, but as it is our current lang of the month, I figured I'd give at least a half-hearted try at it.

l=length r a b=if l a>l b then a else(a++r a(drop(l a)b)) 

Edit: Try it online!

A bit longer than I'd like, my first idea involved the recursive return being r(a++a)b, but I realized that didn't work unless the correct number of repetitions was a power of two.

Curry, 57 42 bytes

This being my first Curry answer, I'm pretty certain its not quite optimal, but as it is our current lang of the month, I figured I'd give at least a half-hearted try at it.

l=length a!b|l a>l b=a|1>0=a++a!drop(l a)b 

Edit: Try it online!

A bit longer than I'd like, my first idea involved the recursive return being r(a++a)b, but I realized that didn't work unless the correct number of repetitions was a power of two.

Edit -15 bytes from some good tips by WheatWizard