Restoring a Postgresql database
What you have is a physical dump of your database, not a logical dump.  So you can't reload it using psql.

What you would do is copy the files over to a new server (don't move them, keep a clean copy for future efforts) which has the same OS, architecture, and version of PostgreSQL, and try to start the database.  If the database were down while you did the rsync backup (and if you rsynced all the necessary files, and whatever crashed the server didn't corrupt things in the process) then the database should come back up and automatically go through its internal recovery process, get to a consistent state, and reopen.

If the database were running during the rsync, then it is very likely that starting it up will fail, or that it will report success but the data will be corrupt, perhaps in hard to detect ways.

Rebuilding it from scratch might be the best option, as then you have a known-good state.