There's no such thing as "the service injected from google-recaptcha".
The recipe you've linked creates a service inside the Symfony project you install the library, it doesn't define a service itself.

I can't see how this could be better than having an explicit service defined by this bundle.

The recipe I linked create a service for ReCaptcha\ReCaptcha here and becaptcha creates a service beelab_recaptcha2.google_recaptcha so there is 2 instance of "ReCaptcha\ReCaptcha" .

My issue (if I recall correctly it's a bit old) is that when I used ReCaptcha\ReCaptcha in a controller I expected to get the beelab captcha instance and got the google/recaptcha instead but feel free to close this issue since It can now be easily fixed with #[Autowiring] attribute in symfony.

I see the problem: the user should not apply the recipe from Google.
Probably we should advise the user in the documentation about it.

Do you mind to propose a PR?