You mention you are in the EU. That's important because the GDPR applies. Even if you are working for a US company.

The details come down to what exactly the software is spying on (I won't look at their website): if it's too invasive, even on a company-provided computer (as many other commenter suggested), it can run afoul of the GDPR (i.e. illegal). There have been some cases already on that [1], and looking up some of them might prove to be a very effective negotiating strategy against that.

[1] quick search on Google: https://www.complianceweek.com/data-privacy/employee-monitor...