Q.How To Prevent Roots From Growing Under Sidewalks Or Out Of Boundaries
How deep do the Buford holly roots grow?

Certified GKH Gardening Expert
These roots will send adventitious shoots out on occasion. They will seek any area that is suitable for them to send a shoot, and gaps in concrete are perfect for this.
Sealing those areas off, and maintaining some of the cracks will eliminate most of this, outside of hand-pulling and chemical control.
The good news is that these are not very destructive, however they are taking advantage of a place to send a shoot. Being a Chinese Holly, these will be more prolific than our own native types.
https://www.gardeningknowhow.com/ornamental/trees/tgen/problem-tree-roots.htm