The junk at the top of the screen sounds like it could be https://github.com/dakra/ghostel/issues/495 and it should be fixed on later versions. But maybe you're seeing another bug. The tricky part is replicating the libghostty-vt internal data into an Emacs buffer while only replacing the parts that need to be replaced. We have property based tests to exercise this a lot, but sometimes things slip through.
The latest released version as I'm writing this should have improved lifecycle handling, so maybe it also fixes some of your issues.
As you say, the project is still in the early phase so hopefully, we can iron things out over time.