Isn’t this the exact opposite of what they were trying to achieve with GDPR?

Not really. I'm sure many people would like that to be the case and fervently believe it to be so, but it's really not.

The GDPR gives people certain rights over data relating to them. It's a bit similar to copyright in that regard. It's different rights and different data but still. For example, you have the right to erasure of that data. Part of the justification for "chat control" is, ostensibly, suppressing the non-consensual sharing of images of minors. That is enforcing the GDPR.