Inside the Oscommerce folder there is an upgrade_guide called upgrade-230.pdf.
there it sais
If you wish to upgrade to a full v2.3 version, perform only (SQL) Database Changes and use the database with a new v2.3 installation.
But how do I make those Database Changes to use it with a new v2.3?
I think I have to manually compare database schemas and modify the old site's backup .sql file (adding/changing fields, adding tables, etc., to match the schema and fixing the corresponding INSERT statements to match). Then you can simply replace the new installation's database with the restored old one.
In the file there are only some SQL-commands to create the action recorder:
CREATE TABLE action_recorder ( ...
What else do I have to change in the old database backup?