Remove deprecated default_database config value

[MasterOdin]

This is an issue to track removing this deprecated value, targeted at doing it for 0.14, so that it is not forgotten for a couple of releases, which has happened a couple of times so far with deprecated things.

A PR should only be made to do this once 0.next has been merged into master, 0.13 released, and a new 0.next branch created to track 0.14.

[MasterOdin]

For follow-up on this from discussion elsewhere, #1890 made it so that a deprecation warning will be triggered when using this value in 0.13.0 and then support for it will be removed in 0.14.0.