When designing a scalable modern cybersecurity architecture, what are some key data protection/privacy considerations to account for — especially in a multi-cloud environment?

When it comes to big environments, my focus would be on Governance, huge installations, distributes over multiple data centres and more than one cloud provider tend to get lost in complexity.
Get a clear inventory of systems and data, define clear accountabilities and responsibilities and a structure to prove compliance top down.

Can you talk a little bit more about what you mean by multi-cloud environment? Multi-SaaS for workforce enablement? Multi-IaaS/PaaS for development and delivery of your own SaaS? Both? Something else?

data classification and sesnsibility is the main to look after.