Every requirement of ISO/IEC 27001 that speaks of information security must be read as extending to the protection of privacy as it may be affected by the processing of personally identifiable information, so the management system is judged against privacy risk as well as security risk throughout.
ISO 27701:2019 5.1 is one control. If you already hold one of the frameworks below, a reviewed crosswalk already says how much of ISO 27701:2019 your existing evidence covers. Hold SOC 2 and 58 of 108 ISO 27701:2019 controls already carry evidence.
Each report names every control your existing framework evidences, every one it does not, the reasoning behind each claim, and the claims that were argued against and rejected. 289 were rejected on the SOC 2 pair alone.
The graph holds this control, the 0 it maps to, and the evidence behind each claim, over MCP and REST.