> what is the compatibility store for third party components/themes based on bootstrap.

I can't speak to components, but for themes there's already a migration guide, and I'd expect to see tools that help with the conversion since they're conceptually similar.

https://v4-alpha.getbootstrap.com/migration/

> will these third party components need to be re-written and support multiple bootstrap versions?

They'll need to be updated, but it's a one way trip. It wouldn't surprise me to see popular themes maintain Bootstrap 3 and Bootstrap 4 versions in parallel for a while.