In which file does an extension register its own PSR-15 middlewares for TYPO3?

TYPO3 reads Configuration/RequestMiddlewares.php from all loaded extensions and builds the middleware order for each stack (frontend or backend) from it. For each middleware you specify a unique identifier, the class and, if needed, before and after so that it runs at the right position in the chain. Services.yaml is a common misconception: it controls dependency injection, i.e. how the middleware class is instantiated, but not whether and where it is hooked into the request flow. Configuration/Backend/Routes.php registers backend routes, not middlewares.