She started the clan, certainly, but within any group of people, family lines sometimes die out. There will be a lot of genetic ebb and flow within the clan as newcomers marry in from outside, as people leave the clan, and so on and so forth. We don't know how many people there were in the Hotgo clan before it was annihilated, but for it to be considered one of the 51 Xaela clans it must have been more than just a family or two. There may be no direct lineage between Mide of the past and Mide of the present.
There doesn't seem to be any lower-limit to how small a clan can be. There are some with thousands of members, and others that consist of like two yurts. Moreover, the striking blue hair of Mide and Dayan is a distinctive feature of the Hotgo clan, every member we see has it, and it's a trait that comes from the two of them.

As for the codex, we're told that the two founders of the tribe did emerge from Alexander carrying it. In fact it's specifically said that the fragment you give to Alex's coeurl just a few moments before discovering it's existence in an ancient legend is an absurd paradox. Basically, we're given every reason to believe it's the same object in a time loop, and and zero reasons to think it's some recreation at a later date.

Instead of questioning the circumstances, it would just be easier to suggest that it's made of some magical, non-deteriorating material. Mide and Dayan's genetics traveling in a loop could also be explained as being possible due to the nature of foundational matter being aether. The laws of physics aren't the same, so I'm not sure there's reason to question things which would be logically impossible from our understanding of our reality.