> The ECHR has ruled that it is not a violation of the convention on human rights, that does not override national law that limits employers if it exists.

It doesn't override national law, but national law is pretty consistently clear that employers have this right as well - that's why the case was before the ECHR in the first place.

You claimed that specific rules the poster you replied to mentioned aren't relevant due to the ECHR decision, and that's just not true. E.g. here in Germany, an employer needs to explicitly forbid private e-mail to be allowed simple access to employee mail, which is why basically everyone does that, often allowing private internet use to access webmail instead. (I've also seen employee agreements where there's different rules for specific folders: a private archive folder is never accessed, work-related folders can be easily accessed and e.g. looking at new mail in the inbox is allowed if it's done under supervision and e-mail that's clearly recognizable as private isn't opened, since private mail was hard to avoid in the specific case)

This is something were you likely can not make useful blanket "in Europe" statements.

Again, it depends on individual agreements. If the employee is not allowed to use his work company mail for private stuff, he has no reasonable expectation of privacy that goes beyond obvious cases. Like, for example, if your wife sends you a mail with the subject "here are my nudes!", your employer isn't allowed to access the content.