What leverage do they use for lobbying, if campaign contributions are off the tables?

Bribery. I'm only half joking.

There's lots of dark international money slushing around out there that happens to make it into someone's wife's friend's company.

This is one mechanism: https://en.m.wikipedia.org/wiki/Revolving_door_(politics)

The art of lobbying doesn't have anything to do with contributions. They will typically donate equally to all viable candidates and sitting politicians to avoid becoming anyone's enemy.

The leverage they use is their relationships with other politicians to engage in vote trading.

They are still (ostensibly) the subject matter experts so politicians defer to them. This in itself isn’t a problem: they should defer to experts on complex matters. And often these experts are organised in industry interest groups. The problem arises when opposing view-points are downplayed.

In the current case this is done because the industry interest groups backing the legislation are predominantly European content rights owners. Whereas the interest groups opposing the legislation appear mostly organised by non-EU groups, and therefore thus are less of a concern for EU legislators, and potentially don’t have the same kind of immediate access to them.

The politicians are still very well connected with the industry. For example there was somebody who retired from the EU Commission a while ago and immediately went to the board of a company or something. The same shit as in the US just a bit less extreme.