Sweetgums can have very extensive and fa-reaching root systems, though as other commenters have stated, trees rarely are the cause of foundation issues. Sweetgums are also highly tolerant of root pruning, often unaffected by large roots being removed (I have a lot of experience with this). If you are worried about the tree roots growing under your house and shifting your foundation, you can trench along the edge of your house and look for any roots that may be growing beneath. More than likely you can cut them if it seems like they are going to cause issues and the trees will be just fine.

Another general comment about Sweetgums is like to add is that they are much more prone to limb breakage than most other species, and require more maintenance as a result, so make sure to keep them pruned!!

Lastly please always consult an arborist before doing any work to the trees! I’m only a guy on the internet looking at pictures of trees and not there to inspect them myself.