Migrate to updated analysis API

It's been a while since this prototype was written and we should have a look at what has changed in the analysis API over the last two years. KSP seems to be a good reference client that showcases how the API can be consumed, specifically the incremental compilation machinery looks really interesting: https://github.com/google/ksp/blob/319ddffc791afc9e34e1d0b80d323635a6ef06c2/kotlin-analysis-api/src/main/kotlin/com/google/devtools/ksp/impl/KotlinSymbolProcessing.kt