It is not "exclusively the right". The social democrats strongly voted in favour of chatcontrol. If there's anything all EU bureaucrats are agreeing on, it's that they need more power.
European social democracy hasn't been left in some time apart for maybe in words.
Regarding EU votes it is fun to always see the same division: people from countries where there is still a left phalanx of the social democratic party always seem to have people (who are always the same) voting with GUE/NGL.
https://mepwatch.eu/9/vote.html?v=134463