I'm sorry for not using any template but none apply.
After filing #4705 I investigated and the reason for the missing parent property is that there missing visitor keys (in the issues case implements for TSInterfaceDeclaration).
As such ESLint does not traverse the child nodes and therefore does not add the parent property.

I built the ast spec and compared the "enhanced" and TypeScript-only node types and found more missing keys.
The missing keys are:
MethodDefinition: typeParameters
TSInterfaceDeclaration: implements
TSNamedTupleMember: label
TSEnumDeclaration: modifiers
TSModuleDeclaration: modifiers

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