The conclusion of the 2nd Season of Discovery shows that all reference to the USS Discovery, its missions, personnel and technology are expunged from the record of the Federation.
In Universe this extends to the very existence of the crew as historical fact. Spock appears not to have a step-sister, rather than having one that died or disappears in some other incident.
The record of what happened to the Defiant would be removed in the same purge.
Regulation 157, Section Three, requires Starfleet officers to abstain from participating in historical events.
Any residual trace or knowledge of Discovery's data, or the time suit, offers a foothold for those who might not see how critical, how deeply critical, that directive is.
Therefore, to insure the Federation never finds itself facing the same danger, all officers remaining with knowledge of these events must be ordered never to speak of Discovery, its spore drive, or her crew again.
Under penalty of treason.
Additionally, the journey of the Defiant to the Mirror Universe, and back in time, represents a stable time-loop featuring the Discovery crew. Without the Defiant reaching the past of the Mirror Universe, the course of history there would be significantly changed and given the cross-over back to the main Universe of Gabriel Lorca and Philippa Georgiou, the history of this side would be affected as well.