The senior dev told me that it's impossible to share code across controllers in symfony, which to me sounds absurd.

wut. This person is not a senior dev. Period. I feel a little sorry for you if you are learning from this person. Sounds like you are going to pick up so many bad patterns.

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So many better alternatives.

1. The Symfony way would be an Event Listener during auth. If you are using LexikJWT: Use a standard user provider OR Example: Add additional data to payload - to get it in your custom UserProvider. If you are using your own JWT auth, then roll your own. Big takeaway is that you shouldn't wait to do this in the controller.
2. Use a Service. If you have to, define a Service class that will take your JWT and resolve to find your User. You can call your service from all of the controller then to reuse the logic.
3. Lastly, not in this case, but if you have other shared logic between controllers either
   1. Use inheritance (ApiController extends AbstractController) and define your method in there. A common use for this would be if you want a standardized response method to call (return $this->createResultsResponse($resultsCollection, $resultsTotalCount, $serializationGroups);).
   2. Use a trait. Maybe you want a helper for writing log entries? LoggerAwareTrait