My understanding is that you have an attestation de dépôt de demande de renouvellement de carte de séjour, i.e. an acknowledgement that you have made a request to renew your residence permit. Unfortunately, this document doesn't really help.
Cette attestation n'est pas un document provisoire de séjour. Il ne justifie pas de la régularité de votre séjour.
“This attestation is not a temporary residence permit. It cannot be used as evidence that you are in the country legally.”
If they take more than three months (not two) to process your application, you should get either an “attestation de prolongation de l'instruction de la demande” (attestation that the response to the application has been lengthened) or ideally an “attestation de décision favorable à la demande” (attestation that the application has been approved). For a renewal, both allow you to stay in France and work.
If you can apply in person at the (sous)-préfecture, then someone will check that you've submitted all the required papers on the spot, and they will deliver a récépissé de demande de renouvellement de titre de séjour. Unlike an attestation, a récépissé does allow you to stay in France. It also allows you to work in most (all?) cases where the carte de séjour will allow you to work.
The list on the French government site correspond to the list of documents allowing entry into the Schengen area. You can enter with an attestation de prolongation de l'instruction or a récépissé but not with an attestation de dépôt de la demande. (Some countries' temporary documents don't allow entering through another Schengen country — this is one of the few exceptions where you can't enter the Schengen area wherever you want — but France's temporary documents are recognized by the other Schengen countries.)
I have no idea if it's possible to apply in person in the post-Covid era. The procedures depend on the préfecture. Unfortunately, in many places, you need an appointment and it's effectively impossible to get one.