– Does age assurance create a risk of surveillance?

No.  The essence of age assurance is proving your age without revealing your identity.  Primarily, that is about not revealing your name to the age-restricted websites or apps you are using, but this also extend to using privacy-by-design to prevent anyone linking a single user across multiple services through the means they used to prove their age.  This is why, led by the French data protection authority, the CNIL, “double-blind” architectures are now favoured where not only can the user not be identified by the platform, but the age assurance provider does not know which platforms the user accesses.  These rely on encrypted ‘zero-knowledge proofs’ of age each of which is unique so they cannot be used to match a user across different sites.