I'm not familiar with EU law, but reading Title II article 7 and 8 makes me feel this could be an optimistic interpretation of what the Treaty of Lisbon guarantees. I'm sure the supporters of chat control would love to argue something like "ChatControl respects the private communications of an individual by protecting how the data is processed to ensure only the legitimate basis of processing the data is incurred by the law" in court.
I would hope the EU courts would disagree, but I'm not sure if anyone can say until it's tested directly.
Even the EU council's legal service thinks the law as-proposed is probably incompatible with Article 7 and 8:
> The CLS concludes that, in the light of the case law of the Court of Justice at this stage, the regime of the detection order, as currently provided for by the proposed Regulation with regard to interpersonal communications, constitutes a particularly serious limitation to the rights to privacy and personal data protection enshrined in Article 7 and 8 of the Charter.
https://data.consilium.europa.eu/doc/document/ST-8787-2023-I...
I think there are variants of the ChatControl proposal which were clearly problematic, but the different variations of the proposal try to toe the line since. This report talks to the 2022 era proposal.