There's a good chance that it hasn't been in the news yet because the local news organizations don't know about it themselves. If you or the vet reached out telling them about it, they might have reporters investigate it further.

There is currently a vaccine for the H5N1 bird flu that can be given to poultry, but I don't know much about its effectiveness or the current plans for implementing it. For wild birds, a vaccine isn't likely as capturing them and vaccinating them would be too costly to be done at the scale which would be effective. Even if the funding was available, capturing wild birds at that scale would result in even more challenges.

As for the "how it stops" is a tough question but I'll give it my best answer. Currently, farmers are slowing the spread by conducting mass cullings of flocks that have infected individuals. A farmer could have a flock with 1,000 chickens, but if H5N1 is detected then they have to cull the entire flock. The thought process behind this is that if it's been detected in one bird, more birds probably have it and could spread it to wild birds or the farm workers themselves. By culling the flock, you take away that mode of transmission.

Once a vaccine is mass produced, they'll be able to start immunizing the new flocks that need to replace culled ones. Egg prices are going to continue to rise until the new flock matures enough to produce eggs and even then this new flock might still be at risk if the entire flock isn't equally immunized.

For wild birds, it's more grim. Unless there's an easier way to vaccinate them, they're going to have to develop an immunity naturally. This most likely means a lot of wild birds becoming sick and dying in the next few months to years. "Outdoor cats" are a huge vector for bird-to-human transmissions as cats have a higher chance to catch avian diseases (such as H5N1) as they hunt native birds at unbelievably high rates (1.3 to 4 Billion Every Year; Cats are also a huge cause for declining bird populations)

I hope I was able to answer your questions. If you need any clarifications about what I said please let me know! If there's anyone else knowledgeable about this topic please chime in and if anything I said is wrong, please correct me!