Thank you @wouterj.

In my User I had to readd the old method:

    /**
     * A visual identifier that represents this user.
     *
     * @see UserInterface
     */
    public function getUserIdentifier(): string
    {
        return (string) $this->email;
    }

    /**
     * @deprecated in Symfony 5.3
     */
    public function getUsername(): string
    {
        return $this->getUserIdentifier();
    }

As I understand it, I could remove the new method that will be re-introduced for the 6.0 BC?

yeah, the getUsername will be removed from the interface in 6.0 (and so you will be able to remove it from your class implementing the interface). Deprecation-free code won't use this method in 5.3+ (using getUserIdentifier instead)

As I understand it, I could remove the new method that will be re-introduced for the 6.0 BC?

Don't remove the new method. Keep both methods for now and drop getUsername() once you migrate to Symfony 6.