connections: Use internal migration tools

Created by: efritz

This PR updates all internal uses of the database to use the new migration utilities. See https://github.com/sourcegraph/sourcegraph/pull/28650 and https://github.com/sourcegraph/sourcegraph/pull/28150 for similar PRs replacing golang-migrate in sg and the migrator service, respectively.

This incidentally moves migrations out of dbconn completely, and into the connections/{test,live} packages.