Again with that fictitious label with zero legal meaning. It was coined for Richard Jewell by the FBI. Despite hit TV shows, there is no such legal thing as a “person of interest”.
He is a “suspect”, because reasonable suspicion indicates he may be be involved in her disappearance.
I’ve known a couple decent guys from the FBI in California and I once asked about the ‘person of interest’ thing and one of them said it could be applied to people who were possibly witnesses, bystanders, suspects, or maybe just people whose presence at or near a scene needed to be explained. Until the FBI had more info it’s a useful term to apply to someone they need to talk to.