Aria is the only one with memories of her last life and it's a power of theirs, it's not well known and most people think it's a world without magic in-universe, but some very few people, like 0,0001% of humanity can have powers, and even then they only trigger in really stressful or death and life situations, hence Aria getting her ability to get back in time at that moment.
We do see someone else with powers, a man with the ability to teleport, but these powers are so damn rare that only very select people like the members of Royalty even know that powers are a thing, Mielle, for example, has no superpower so she isn't looping back, no one else is, it's Aria's exclusive power as she is kinda the equivalent to a X-Men mutant.