Should I be worried about connection attempts to "Private Network"?

It's perfectly normal to have a "Private Network", yes.

"Private Network" in terms of Little Snitch means that the communication has occurred between network addresses that are usually not routed on the internet. This means that the private network is usually either devices on your local network (i.e. in your own house for example), or devices on a private network you connect to (for example a work VPN with servers that have these addresses).

In general, there's nothing particularly "worrying" about private networks. There's no reason to be paranoid.

Whether or not the actual traffic is benign or malicious requires further analysis. You would need to know more about the specific communication, the devices on your local network and any other private networks you connect to.

As this type of knowledge is harder to come by for non-IT professional home users, it can be that Little Snitch itself becomes a source of needless worry - unfortunately.