An interesting interpretation, indeed.Exactly. Europe claims to protect privacy but in reality they want access to all the sites you visit and what you do. It isn’t just the carriers either, it is the governments also who want access.
First, "Europe" (the EU, European Commission) has not banned or threatened to ban Apple Private Relay. Four carriers operating in Europe (T-Mobile included) have sent the European Commission a letter essentially stating they do not like Apple making it more difficult to spy their customers. The European Commission has neither replied nor taken any action.
Second, the background of digital sovereignty in Europe is worth understanding. The situation in the US has been called "surveillance capitalism", as companies are quite free to monetize customer (or even customer's) data. China has its own state-controlled model. The EU does not want either, and the underlying idea is to give individual citizens as much control over their own data as possible.
Of course, different companies and governments want to have access to our data, and not everyone is happy with the existing and emerging EU regulation. Quite obviously, those four telcos are not too happy.