I think you found a common stumbling block. The tutorial people follow may say to run pg_dump and many people would assume you're running it from the old version.
On Debian (and probably most of its derivatives), the package manager will not remove any running PostgreSQL versions and will let you have multiple versions side by side. It also has its own tool pg_upgradecluster, which can perform the upgrade using pg_dump+pg_restore or pg_upgrade (optionally with link or clone options).
Yes, and usually, it means you need to use the full binary path unfortunately (because debian wrappers embedded in the package select the version from your 5432 cluster).