So is the migrator tool working now without errors to migrate your data into PostGres?
Not sure what you are trying to achieve with the h2 console (and support for this is really separate to anything GoCD related) but h2 versions have very limited limited backward compatibility. They don't use semver.
So your H2 DB from GoCD 20.4.0 and earlier won't be usable with h2 console 2.x if this is the version you downloaded. it may also have issues with h2 1.4.x rather than 1.3.x. if you want/need to browse with the h2 console you'll probably need to use the appropriate version for the database you're trying to open.
For wider context, the need for this forced db migration at GoCD 20.5.0 is partly due to such H2 breaking changes in H2 1.4.200. since GoCD did a migration in that version from H2 1.3 to 1.4 all GoCD H2 users are forced to do this migration.
To minimise number of manual migrations needed and give more flexibility to users to switch away from H2 this was combined with an internal GoCD switch to a different db deploy automation tool (dbdeploy -> liquibase) as well as open sourcing and inlining into GoCD core the previously commercial 'extension' support for running with non-H2 databases. The migrator tool was written to support all of these breaking change migrations in one GoCD upgrade.
-Chad