Infinite loop when using Doctrine transaction middleware with #[ApiResource(mercure: true)]

[toby-griffiths]

API Platform version(s) affected: 4.0.16

Description
We have a brand new project where we've just set up messenger with the doctrine transaction middleware. When attempting to create a new Greeting we get stuck in an infinite loop.

How to reproduce
Clone this repo, and follow the README steps.

Possible Solution
Not 100% sure, but maybe have the Mercure listener remember that it's already processing an entity, so it doesn't attempt to do it repeatedly. Happy to submit the PR if this is the preferred approach, or another with some guidance to how.

Additional Context
n/a