Unfortunately I had a servercrash without a backup of the dump of the database (I know.)
A Painful Truth:
Any Data that you don't have [at least] two copies of is Data you don't care about losing.
That is what's happened here.
... data on the tapes is from an Mysql server and cannot recover into the postgres database?
The data files used by MySQL are nothing like the ones used by PostgreSQL.
To all intents and purposes, they contain completely different "languages" and are only "translatable" through "portable" format, like SQL.
There is no way that you can just put data files from one DBMS "into" another one and expect it to work.
Now, a [mysql]dump of the MySQL database would probably be plain, SQL text.
You might stand a chance of modifying that SQL to work with PostgreSQL - yes, SQL dialects are different, too!) and import that but, as you say, you don't have such a Backup.
You're only real chance here is to recover the data into a MySQL instance and then start worrying about how to migrate it to Postgres.
Given that Bareos used to support MySQL and now don't, it would be reasonable to expect them / its suppliers to provide its customers with tools/methods to migrate away from MySQL.
Oh wait, perhaps they already have.