What's the standard naming convention for a property's backing field?

There is no code convention standard for TypeScript. Since it is a superset of JavaScript, following JavaScript code conventions would probably be the correct approach. In such a case you would use an underscore-prefixed property _status. Idiomatically, this also matches the compiler’s use of an underscore-prefixed _this for compiled arrow functions and underscored-prefixed _super for superclasses.

In C# as well as TypeScript we use private _status. In C# the property will be Status. In TypeScript as you mentioned it is status