”The last recorded exploration was over a century before Doctor Vellek was even born.” That does potentially raise the question of how Burnham would have been so familiar with Lyrek in the previous episode, though of course she and most of the rest of the Discovery crew might have been alive before Doctor Vellek’s birth.
We've seen that in her one year as a courier, Burnham learned everything about every planet because of secret criminal space knowledge. Even if the last recorded exploration was that old, presumably space pirates with their gritty streetsmart know-how have some sort of Mos Eisley medieval market nearby.
They seem to be saying that the solid form is a sort of defense mechanism, like a snail shell or an opossum playing dead (or maybe an environmental one, like that it prevents the jelly form from losing too much moisture in a warm environment). It's difficult to maintain, and implies you're in a position of retreat or weakness. Now that the Breen presumably have no predators and no environmental necessity for the solid form, it's seen as a cultural taboo.
While I'm a little bummed the Breen aren't the space-arctic-wolves I imagined them as during DS9, I think it's an interesting idea. I do always like when they describe how cultural practices in a particular species comes from how they exist in the ecosystem of their home planet, like the Kelpiens (Saru and the Kelpiens being for me, Disco's most successful addition to Trek canon).