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It's actually quite simple - an offline solution is technically incapable of reporting your spending patterns because ... well ... it doesn't connect to any network. It's the same as physical cash really, your banknote cannot report where it's been since it does not connect to anything.

You're making a jump from transparency to Free Software, but it's a jump too far.

It's sufficient to have open (and trustworthy) protocols. Software will follow.

Serious question, if it was free software, how would they prove they're actually running it (unmodified)?

The EuGH (European Court of Justice) is already in power to check the EZB. It could also check the software.