If you place your personal laptop let's say on the kitchen table and connect it to your wi-fi and your work laptop on your desk and connect it to your work (probably using your wi-fi and a VPN) There should be no way that your professional laptop can know what your personal laptop is doing.
If it does, that would be considered hacking/invasive and certainly against EU law.
Now... I don't think your employer does it. It is a lot more likely, that your setup of computers at home is not as strictly separated as I described. You probably have your personal laptop somehow connected to your professional laptop. Either because you use it only as a second monitor as described, or maybe because it's connected to the work VPN, too.
Please also note, that if you are logged in with for example your Google account in the Chrome browser on both laptops, it will synchronize between those two. You can turn it off, but if you don't, yes, your employer will find out what you did on your personal laptop.
Again, it is very unlikely that your employer has any kind of criminal hacking activity going on, it is very likely that you get something wrong in your own setup of devices and online accounts.
If you have a specific question about your specific setup, you can probably get help on Information Security SE. Be prepared that they need a lot more technical details to give you a good explanation for what happens.