The European Convention on Human Rights has an article about privacy (article 8). Note that this is from the Council of Europe, which is not the same as the European Union: non-EU member states such as Russia, Turkey, and Azerbaijan are also part of the Council of Europe and therefore the ECHR. I'm not sure if you first have to go to a lower court, but the European Court of Human Rights is the authority on this (commonly mistaken for the European Court of Justice, but they are distinct entities).
According to this ruling of the ECtHR, it is not illegal to monitor your employees' communications per se. However, the monitoring has to be:
- for legitimate purposes ("the employer had only accessed the account in the sincere belief that it contained only messages of a professional, not personal, nature"),
- proportionate ("it was the only possible way available"), and
- communicated to the employee (or, if the monitoring is not announced, at least the restriction on personal use should be communicated, for example through company policy).
In the European Union, there is also the GDPR, but this does not change much. It applies to your employer the same as any other organisation and basically says that they have to be reasonable about it: collect only what they need, for a legitimate purpose, and tell you about it. I think you should be able to request a copy of any data they collected about you, ask a human to review an automated decision, and your other usual rights. They don't need your consent to start collecting data, as Esa Jokinen already commented: "GDPR doesn't even require consent to handle PII data, but the consent is just the last option when there's no other legitimate reason to process the data." In fact, your employer probably cannot ask you for consent: because of the employer–employee imbalance of power, the consent would probably not be considered to be freely given (where this article mentions "The GDPR states", I think they are referring to recital 43).