Not any website. If it is purely private and non-commercial you don't have to.
Also, it doesn't have to be "all your personal information". Your Name is required and an address where you could be served with court papers. A P.O. box is not required, but the address where your company is located is fine. It doesn't have to be your private home address. An email address is required, but that again doesn't have to be your private one. It just has to work. A few other things are required, e.g. where your LLC is registered if it is an LLC.
> If it is purely private and non-commercial you don't have to.
Unfortunately, this does not include a lot of websites that most people would classify as private. For example, a blog still needs an Impressum.
In addition, you will even be classified as commercial, and therefore require an Impressum, if you don't make any money, for example if you use ads to (try to) pay the hosting cost.
> A P.O. box is not required
In fact, you'll have to pay a fine of usually 5000€ if you use a P.O. box without a summonable address.
I've got an imprint, including my mobile phone number, on my partly personal, partly business website for about 15 years now. In this time I have not received any calls or unwanted mail on this address. Not a single one in all those years.
Maybe your website is not popular enough. I had a website a few years ago (not anymore) and since then I receive about one call per week of "Microsoft" employees asking me to install some backdoor software.
Well, I can't complain about visitors and views and the resulting business out of that. Maybe I'm just very lucky, but it's not such a big deal as OP wants it to be.
You also need to make the links obvious. The light grey on white they do on that page likely isn't compliant, and neither is their privacy information ;)
Also, it doesn't have to be "all your personal information". Your Name is required and an address where you could be served with court papers. A P.O. box is not required, but the address where your company is located is fine. It doesn't have to be your private home address. An email address is required, but that again doesn't have to be your private one. It just has to work. A few other things are required, e.g. where your LLC is registered if it is an LLC.