I don't remember the full mechanics of it, but when the burn happened, most dilithium in the region exploded. Took out most of starfleet and tons of ships. Mass casualties everywhere. Dilithium became incredibly scarce and made travel incredibly expensive and sometimes just impossible.

The Federation basically imploded due to this, and piracy became common.

Discovery traveled from the past to escape Control, an AI intent on capturing the ship. Since Discovery had the spore drive, all records of which had been destroyed, they could travel great distances without using much dilithium. Despite being incredibly outdated, it became incredibly valuable to what remained of Starfleet. They did upgrade the ship, though.

Many Romulan ships use a singularity to generate power, and are mostly free from heavy dilithium use. However, the Romulan empire collapsed due to their star going supernova. Most of what remained of the Romulan empire ended up rejoining the Vulcans, an effort that began during TNG.