The ccTLDs of the EU member countries are a very good idea if you’re an EU citizen because they have built-in privacy for individuals (they don’t publish their info in WHOIS) and are also subject to GDPR.

Still overthinking, I found CZ NIC might be interesting for security, but definitely not privacy.
www.nic.cz/page/383/faq/

Protect your domain or contact from unsolicited changes. Block them at CZ.NIC Association and no change will be possible through the registrar. If you want to change anything first it will be necessary to unblock a domain or a contact with CZ.NIC. These blockings are confirmed by an electronic or certified signature. Nowadays it is possible to block or unblock a domain online in the Domain Browser (on www.domenovyprohlizec.cz) - this applies only for validated accounts mojeID

On that website, it also mentions possibility to use EU ID for that purpose, so I’d be fine. But it doesn’t allow hiding my address.
Indeed - “Why do you show my home address on your website? Can I disable it?”:

All personal information is automatically hidden, except for the name of the organization, the name of the individual and the postal address. It is also possible to hide the postal address information if the contact is registered to a natural person (the Organization field is not filled in) and at the same time is managed via the MOJEID service and the contact is validated.

But the requirement to validate is:

As part of improving our services, we have replaced the former validation process with a new one — linking the account with the National Point for Identification and Authentication (i.e. getting access to public administration services), which also includes identity verification.

Which is this thingy: portal.gov.cz/en

Finally, if trying to sign up there I get to a FAQ that states this for question if it can be used by foreigners:

Yes, you can if you have in the Czech Republic permanent or temporary residence, visa sticker, temporary international protection or granted international protection.

So it seems while I could get better security than with other registries, my home address would be made public.