Merge changes from experimental

For a while we haven't been able to upload to unstable because of the freeze, but now buster has been released so we're no longer forced to use experimental for big changes such as rebases.

This MR takes all the work we've done in experimental and brings it back into unstable so that we can build upon it.

I'm currently working on updating the package to 5.6.0, and this is an obvious step in that direction. I'm not sure whether we want to upload 5.3.0 to unstable first and then move forward with the update to 5.6.0 or whether we should just jump straight to 5.6.0: I'd probably prefer the latter to avoid spending additional time on an upstream version that's already obsolete.

Either way, these changes can be merged right away no matter what choice we make; if we decide for the latter, it'd be awesome if 5.6.0 could be imported right afterwards.