Which law are referring to? I work in such an agency and I’ve never heard of such a thing
Well, in Italy the "IRS" (Agenzia delle Entrate) is not allowed to cross-check banking statements with its own data from Tax Returns.
Whenever anyone proposes to allow it, the members of the informal "Party for Tax Evasion" scream and denounce the descent towards "Taxation Fascism". It's so pathetically cheeky, that it feels a bit endearing (how dare them, what rascals!)
Dunno about Germany but in Belgium there is Crossroads Bank for Social Security which effectively controls the flow of information between various social security and public health organizations: https://www.ksz-bcss.fgov.be/
In its current form, it's a set of SOAP or REST APIs that your organization gets access to after completing paperwork about your needs.
It was established by a 1990 law [1].
There is also a similar legal and technical setup for information on companies [2] where most information is public, and the register of residents [3] which is even more guarded.
[1] https://www.ksz-bcss.fgov.be/fr/page/loi-du-15-janvier-1990-...
[2] https://economie.fgov.be/en/themes/enterprises/crossroads-ba...
[3] https://www.ibz.rrn.fgov.be/fr/registre-national/