In The Netherlands, employees enjoy a reasonable level (much stronger than this scenario) of privacy even on company equipment [1]. That is: the company cannot randomly access an employee's mailbox. Of course, in case of employer-employee dispute, things become hairy - but even then, the company is not allowed to go on a fishing expedition. Though they can go on a confirmation run, looking for specific evidence, e.g. mail from Glassdoor.

Don't know about other EU countries, but at least NL deviates significantly from the sketched scenario.

[1] https://blog.iusmentis.com/2017/11/22/wanneer-mogen-mailbox-...