I could potentially see him having co-opted it, but equally just seems that he wanted to propagandize the notion of Rome being revived from his reign, hence "Restitutor" and "Corrector" being a common epiphet in his titles.
Speaking of Aurelian..
Going to go on a rant. I have seen several times this claim that Aurelian persecuted Christians but it makes little sense to me. The persecution of Christians comes from two sources, Lactantius and Eusebius. Both were very focused on exalting Constantine and heaping praise on him and vilifying anyone who might challenge the narrative. Also they vilified Domitian with the same slander commonly attributed to him which always adds more dubiousness to the claim. The main thing, however is that Constantine was a strongman emperor who reunited a divided empire, modified the currency to deal with inflation, and pushed for a monotheistic religion. These are things which can be attributed also to Aurelian. The glory of Constantine seems less impressive when Aurelian had done these same feats. Given he was already not popular with the senate (Which never is a good measure for how good an emperor is, just look at Domitian and Hadrian), it would be easy for them to smear and exaggerate Aurelian's faults to make him look lesser to Constantine. There is no reason not to believe a lot of the evidence of Aurelian violently persecuting Christians was fabricated or at least exaggerated to condemn him.
Furthermore there are other recordings of Aurelian helping Christians with local affairs. It also makes little sense why he would try to persecute Christians as a whole group when he was trying to stabilize the empire. Aurelian was an older emperor, he would have seen and remembered Decius' failed attempt at persecuting Christians. Not even the sources biased against him mentioned him singling out Christians like how Decius did. Doing so wouldn't make sense because it would lead to more discord and instability, the last thing he wanted. He also wouldn't want to cut down the tax base any more than he had to. Not that he didn't persecute Christians, even Trajan and Marcus Aurelius signed off on low level persecution. He very likely did sign off on a few low level pogroms to get rid of uppity outliers but otherwise why would he care. He only was in a stable political position for a few months before his death and he focused more on construction and economic projects that were of immediate concerns.
I am not trying to be a fanboy for Aurelian. While I respect and admire him, his economics were actually quite terrible (Rant for later) and helped expedite the end of the empire, but most of the evidence of him being this vicious persecutor of Christians just seems politically motivated and tenuous at best. At worst he acted no different than Marcus Aurelius or Trajan persecuting Christians and the politically motivated Lactantius and Eusebius, eager to have a reason to discredit him, latched onto that.
Maybe I haven't read enough sources, but I don't know. I read as many as I could in late 2021 and while I had a pretty negative view on his economics, I really couldn't find much to really prove what Eusebius or Lactantius claimed, unless they have some source lost to us now. Actually kind of wish a history youtuber discussed this kind of stuff. It's clear when it came to being a commander Aurelian was inhuman, but nobody really discusses his policies in depth which is a shame.