Made a timeline of Columbina's journey. A good portion of these events are theories of course, and not definite official lore.

Theories Long Version:

The Trilune-Authority: I believe it's likely that the Trilune-Authority was hidden in the Frost Moon after it was sent beyond the False Sky, since during "The First Silver of Moonlight," Sandrone scans for the Moons that still have Authority and are alive, and discovers three moons; or rather, the Three Authorities that lay hidden in the Frost Moon. We also know the Moon Goddesses do eventually return to Teyvat without their Authorities, having given it to Columbina as they have no way of defying the Heavenly Principles banishment of the Three Moons. See the "Space-Time in the Moon's Reflection" section for more theorizing on this.

Luonnotar's Role: We know Luonnotar provides an anchor to which Columbina's soul within the Moon's Reflection will return to Teyvat. I assumed that the conditions required for it to trigger was for Columbina's body and authority to be in the same place, thus resonating with Luonnotar which resonates with Columbina's soul in the Moon Mirror, thus bringing it from there, while it still remains there (see Space-Time in the Moon's Reflection for details).

The World-Formula: We know that the World-Formula can calculate the very Fate of Teyvat itself, and was used by Rene, who used it to compute that Teyvat would eventually die with the current era being the last era. We also know that Sandrone would take Rene's research and use it to instead compute Columbina's return and its conditions. Sandrone's World-Formula was "a highly complex algorithm capable of constructing a framework of rules," and is capable of predicting Teyvat's fate, but is unable to predict "outside variables," or "Descenders." Thus, I assume the World-Formula is designed to somehow not only predict fate, but allow for its manipulation, except said manipulation cannot be changed by those already within Teyvat, for this would have already been predicted. Instead, fate can be manipulated by those from outside Teyvat, or Descenders; thus changing the prediction and through it, fate itself.

Space-Time in the Moon's Reflection: Space and Time are both linked in the Moon's Reflection, with one moving forward in this space causing one to move backwards in Teyvat's time, since all movement within Space leads to the Three Moon Goddesses' Prison, which was established during the War of Funerary Flame. I also believe Time also doesn't flow here, since Columbina met (sane) Rerir, Tholindis, and the Three Moon Goddesses, none of whom were sent into the Moon's Reflection at the same time, yet exist there at the same time. It's in my belief that anything that enters the Moon's Reflection has always been there because Time doesn't exist here, but not in the same space, because Space and Time in this realm are one and the same.

Space-Time and Columbina: Since the Three Moon Goddesses exist in their prison which was established during the War of Funerary Flame, this means that any action that Columbina the Trilune Goddess would do to Teyvat from within the Moon's Reflection would occur during the War of Funerary Flame. Thus, Columbina's body and authority would reenter Teyvat during that period; meanwhile Columbina's soul simultaneously exists and doesn't exist in the Moon's Reflection, since it does exist to guide Pastbina, but it doesn't exist since it's already been called from the Moon's Reflection to become Futurebina, and both are true because both don't exist in the same area of Space.



Short Version: Columbina both exists and doesn't exist in the Moon's Reflection, since she exists at the same Time, but not the same Space. Pastbina is guided by Futurebina to become Futurebina, who casts out her Body and Authority in Teyvat's past, creating the conditions for Pastbina to be born in Teyvat's future; and her Soul is cast out to guide Pastbina to become Futurebina. This goes on and on until her Body (Kuuvahki) and Authority (Frostmoon) exist in Teyvat, thus setting the conditions for Luonnotar to resonate with these two to call her Soul back from the Moon's Reflection.



TL:DR - Columbina's entire existence is a case of Stable Time Loop and Schrodinger's Columbina; and she is both her future and her past until she is finally revived to kill Dottore.
A Timeline of Columbina's Journey