Therefore it required that the parliament give its assent to each and any (if I'm correctly informed) legislative act of the EU.

The FAZ article linked to above indicates that the BVerG requires that the Bundestag and/or Bundesrat be consulted on, and give their positive assent to changes in the EU legislative process - and not individual acts.

Specifically, it concerns the so-called bridge-clause, i.e. the transition from the requirement of unanimous decisions at the EU level to a (mere?) qualified majority.

The fact is that what we're experiencing right now is a top-down disaster. -Paul Krugman