Quite the opposite; in case of copyright expansion the large companies you mention are the copyright holders, which are about to be given governmental mandate to steamroll over the citizens even more. Quite the opposite of GDPR which went to protect the interests of individual citizens.
That was fine when they we're dumb platforms, but when they started picking and choosing what content was allowed based on their own interests they really gutted any sort of claim to just being a platform
This sort of thing is just an extension of a very long running feud that goes back a decade or more, driven primarily by the newspaper industries in the EU "core" states. The German and Spanish "Google taxes" were also attempts to change how copyright works on the internet, targeted at Google News entirely to the benefit of newspaper owners, but they failed because Google just either cut deals or in Spain shut down Google News entirely.
So now the newspapers are trying to do the same thing at the EU level, working on the theory that if all EU countries act in concert then Google and Facebook will have to cut the newspapers a big cheque. Early attempts to just change copyright so the act of linking or snippetting requires a license have now warped into this wider attempt to extract money from internet companies via copyright.
There is some political background here too - newspapers can't do this by lobbying national governments directly, because the finances of newspapers is far, far, far down the list of things citizens care about and national governments are all focused on other things. Luckily for them (!) the EU doesn't care what citizen's priorities are and doesn't need to!
Moreover the EU is heavily incentivised to please the newspaper owners because it benefits from unusually positive coverage for governments in the old European media (not so much in the UK or eastern European states). Journalists have largely bought into the narrative that the EU is a glorious positive peace-filled future and as such newspapers in Germany or France heavily weight their scrutiny towards the "legacy" national governments instead. The piper is now demanding to be paid. The Commission is probably worried that if it loses the support of the press then things will get a lot harder for it in future.
In this case corporations like Facebook, Google, et al have stated that they are platforms and can't be responsible for what people post on their systems. At the same time they are selectively removing content based on their beliefs or economic concerns, and not solely under court order.
There are two options. One is to be a dumb platform serving anything someone wants to out up, and thus free from any copyright claims. The other option it to be an arbiter of the content, which means they are responsible for said content and so they are responsible for the endemic amount of copyright violation on their systems.
The companies didn't want to pick their role, so governments are picking for them