31st century

The 31st century was defined in the calendar of Earth as being from 3001 until 3100.

Decades

Daniels is born. By this time, time travel is so commonplace that there are quantum discriminators in every high school desk. (ENT: "Shockwave, Part II")

Daniels, fearing a change in the timeline, transports Jonathan Archer to this time, causing a catastrophic timeline change that wipes out his entire civilization. Returning Archer to 2152 remedies the problem. (ENT: "Shockwave", "Shockwave, Part II")
An Earth vessel travels back to the 22nd century, where it apparently suffers some sort of critical disaster. The pilot is killed in the accident and the pod itself is heavily damaged. It is eventually discovered by the Enterprise NX-01 in October 2152, and Enterprise's chief engineer Commander Charles Tucker is able to reactivate the pod's temporal beacon. Within seconds, the pod, the dead pilot, and the beacon itself all vanish, having presumably being retrieved by operatives from the 31st century. (ENT: "Future Tense")

While on a mission to investigate a "dilithium nursery" in the Verubin Nebula, the KSF Khi'eth crash lands on an astronomical body at the center of the nebula. Responding to the distress call from the Khi'eth, the USS Hiraga Gennai is presumed destroyed when it attempts to penetrate the nebula. Six months later, the Khi'eth sends out another distress call that becomes the basis for the melody. (DIS: "The Sanctuary", "Terra Firma, Part 1")

Most of the Milky Way Galaxy's dilithium becomes inert in what becomes known as The Burn, resulting in millions of deaths when countless starships lose antimatter containment and are destroyed by warp core breaches. The United Federation of Planets is unable to explain exactly what happened, why, or that it wouldn't happen again. Without dilithium, the Federation's presence diminishes to the point where believers in its vision are uncommon. (DIS: "That Hope Is You, Part 1", "Die Trying")

Cleveland Booker and Charles Vance both stated that the Burn happened roughly 120 years ago from 3188 and 3189, respectively. (DIS: "That Hope Is You, Part 1", "Die Trying")

Captain Jean-Luc Picard estimated that the core of Atrea IV would remain molten until this time. (TNG: "Inheritance")

In the Delta Quadrant, a Kyrian historian named Quarren discovers a backup copy of The Doctor. After he is reactivated, The Doctor corrects the distorted view of USS Voyager in Kyrian history and precipitates a new harmony between the Kyrian and Vaskan races. After many years as Kyrian Surgical Chancellor, this copy of The Doctor boards a ship and heads for the Alpha Quadrant to find out what happened to Voyager and his fellow crewmates. (VOY: "Living Witness")

The Federation moves its headquarters off Earth. (DIS: "People of Earth")
Starfleet leaves Earth, and United Earth leaves the Federation. (DIS: "People of Earth")
Titan splits off from Earth. (DIS: "People of Earth")
Ni'Var leaves the Federation. (DIS: "Unification III")
A Federation starship visits Ni'Var, becoming the last ship to do so until 3189 when a diplomatic mission brings the USS Discovery to the former member world. (DIS: "Unification III")
Deep Space 253 begins trading with an Emerald Chain merchantile. (DIS: "There Is A Tide...")

Kyrians obviously have had no contact with the Federation between their encounter with Voyager in 2374 and this time, despite claims by Q that the Federation will have a presence in the Delta Quadrant as soon as the late 25th century as per VOY: "Death Wish".
Going by Data's statement that the energy ribbon from Star Trek Generations passes through the Milky Way Galaxy every 39.1 years, it could be expected to return in 3034 and 3073.
The undeveloped series Star Trek: Federation would have taken place in this century.