Why build a new browser in C++ when safer and more modern languages are available?
Ladybird started as a component of the SerenityOS hobby project, which only allows C++. The choice of language was not so much a technical decision, but more one of personal convenience. Andreas was most comfortable with C++ when creating SerenityOS, and now we have almost half a million lines of modern C++ to maintain.
However, now that Ladybird has forked and become its own independent project, all constraints previously imposed by SerenityOS are no longer in effect.
We have evaluated a number of alternatives, and will begin incremental adoption of Swift as a successor language, once Swift version 6 is released. (More background.)
From their FAQ https://ladybird.org/#faq