Thank you for your question and patience, I’m Tom and I’ll try to help you.
You, your wife and your son will be fine. Your right to stay in the UK is highly unlikely to be in jeopardy.
Because you and your wife have worked in the UK for longer than 5 years, you would be regarded as having “permanent residence”. However, because you have not yet applied for confirmation of your PR you do not actually have a document which formally states that you have it.
So, I would suggest that you and your wife apply for PR (https://www.gov.uk/apply-for-a-uk-residence-card/permanent-residence-card ).
Once you have PR you then have absolute proof of your right to be in the UK indefinitely. This won’t change as a result of an exit from the EU (which is still far from certain and won’t happen for a considerable time).
Your son is entitled to be registered as a UK citizen under s1(3) of the British Nationality Act. This is because he was born in the UK to parents who are not British citizenship or settled (ie. holding PR) at the time of his birth but who have subsquenelty become “settled” (ie. you have PR). I would check that the German government accepts dual citizenship (but I believe they do).
The slight issue is that you do not hold documentary proof of your PR status, because you have not applied for confirmation of your PR status. So, in the case of your son I would wait until you/your wife have had your PR confirmed and then apply to register your son as a UK citizen. Note, this is different to simply applying for a passport because you are applying for registration as a UK citizen:
Once you have obtained a certificate of citizenship for your son, you can then apply for a UK passport for him if you wish.
My goal is to provide you with a good service. If you feel you have received anything less, please reply back as I am happy to address follow-up issues specifically relating to your question.