Did I read somewhere that support for using a VST3 synth as a default synth is coming soon? (2024 BIAB?)
At present, BIAB does not support any VST3 plugins, but yes, I believe they are intended to be in the 2024 release. Logically(!) that would include for the default synth.
There are a few VST host applications around that will wrap VST3s inside a VST2 wrapper, so there are workarounds available today.
Musocity often recommends Kushview Element, partly as it's OpenSource and free. I believe it works well. There are several others.