You can have an anonymized dump like you'd normally do and then branch it. This allows spinning up environments in seconds and without the disk footprint of a new replica or dedicated DB.
The privacy / security constraints stay the same whether you are branching or not.
Anonymizing data is the biggest part of such a workflow. Most prevalent use case that requires production data is for debugging. I guess there is some value in branching non-prod databases for feature development.
Most security teams do not allow prod data in non prod environments, anonymized or not l.
The privacy / security constraints stay the same whether you are branching or not.