These are not the purpose of Short Treks. They were meant to just be webisodes focusing on the shows they were currently producing.
But, if they plan to revisit Burnham and the Klingons in the 32nd century, I don’t see what’s the big deal in having a 30 minute Short Trek featuring Harriman, Demora Sulu, Azetbur and Colonel Worf in the early days of peace between the Federation and the Klingon Empire Something that can be called back to when the Discovery crew needs a reference when meeting the Klingons again, and want to compare their personal experiences.
Similar, seeing how the EMH has lived during the Burn makes sense as a set up to an episode dealing with his arrival/discovery.
Its not any different than the Short Trek of Tilly getting Po some ice cream. Or the schoolgirls having a fight at school before learning of the synth attack on Mars. Or Burnham being told a bedtime story.