Genshin Dragons
I just wanna pair dragons up with Genshin characters, and no one is gonna stop me >:3
The Nexus
Set post main story, assuming that the Heavenly Principles were defeated and forced to cede their rule over Teyvat, now the outer bounds are being governed by the Hexenzirkel while the various lands of Teyvat have their own governments. The false sky has also fallen, leaving Teyvat vulnerable to the rest of the universe.
The Nexus. A phenomenon discovered by Octavia, and introduced to Alice as a potential solution to the Abyss problem. Dragons and dragonriders, battling together against great threats! It was an intriguing thought, and given Teyvat's newfound vulnerability, well worth the risk. So Alice opened a portal, intending to make contact with just the giant Weyr Octavia found- unfortunately, not unlike the Abyss, the Nexus is unpredictable, and took hold of her spell, casting it out across the world.
Portals now opened all over Teyvat, and dragons and eggs could be found anywhere. It's now up to the people of Teyvat to take control of the situation and forge lifelong partnerships with these new beings from other worlds.
Vedvolt Weyr
The grand Weyr Alice had originally attempted to make contact with. She managed to create a stabilized version of the portal spell, allowing each nation of Teyvat to contact this Weyr. Quickly, the governments of the world took control of the situation, establishing background checks on anyone who wants to apply for a dragon through the Weyr. The Weyr, too, had it's own tests, testing a person's character, strength of heart, their courage, and other such means of judgement that all riders of the Weyr have to go through.
Now, in order to get a dragon, there are two methods- either go through the processes to get one through the Weyrs, which are guaranteed to be Bonded and tame, but take a long time and you aren't even guaranteed to get one. Or, take your chances in the wild, and hope the ones you find out there are willing to partner with you.
The Dragons
Thankfully, the dragons that pass through the portals of the Nexus are relatively tame creatures. No mass destruction or chaos follows them, just curious creatures who arrived on Teyvat looking for a potential home. Not all are seeking partnerships, but many do, or are at least willing- if a potential rider can prove themselves. Some can even Bond, able to communicate thoughts and feelings to their riders even without natural telepathy.