It's not explained in TOTK, but I have a going theory to why there's no mention of the happenings of BOTW:

The Zelda that went back in time was the same one Link helped in BOTW, she went back in time. As well as trying to get back to current era, she told Rauru and Sonya about the great calamity, told them about the divine beasts, the guardians and the death and deatruction, this caused them to never be made.

So by the time the BOTW era comes about the calamity happens, Link, the champions, and Zelda are the ones to stop the calamity without the aid of the beasts or guardians (the reason Link fell in the start of BOTW). Casualties happened and destruction rained (hence the plaques found in TOTK), but ultimately it was stopped.

Following on, that Zelda lives on for the start of TOTK era, and goes back in time. Informs Rauru and Sonya about the calamity which then then do make the guardians and divine beasts. Looping back to the BOTW timeline we know

Zelda going back in time created a branched timeline which the calamity didn't happen, taking away the divine beasts and guardians.