Should any liquid, or liquid-like ingredient, be included in the water proportion calculations for bread?
It depends on how exact you feel you need to be.

Rough Approximation

As a general first order approximation, the following ingredients can all be treated essentially as water:


Milk, butter milk
Fruit juice
Fruit puree
Milk, cream, sour cream, creme fraiche and similar dairy products
Even eggs


This is not perfectly accurate, of course, but for many applications it is close enough.

If you want to get more detailed and more accurate, you would have to find out a reasonable approximation what percentage, by weight, is actually water.

Dairy

For dairy products, like cream, this is fairly simple to do, as a second order approximation.  Just deduct the percentage of fat and assume the rest is water. For example, whipping cream which is 36% fat (check the label) is going to be about 64% water.  This is still an approximation as it does not consider sugars and minerals, but it is probably close enough for almost any non-industrial culinary use.

According to the IDFA (International Dairy Foods Association), sour cream is about 18% milk fat, so an approximation of 80% water would be quite reasonable.

Eggs

The University of Illinois provides the following information about eggs:


Whole eggs&mdash;74% water
Whites&mdash;88% water
Yolks&mdash;48% water


Fruit

This PDF from the U. of Kentucky Extension provides composition information, including water percentage, for some common fruits.  Most, with the notable exception of bananas, are in the mid-80 to mid-90% range.  Bananas are about 75% water.

Other ingredients

For other ingredients, you would need to do some research to determine the typical percentage of water.

Example Calculation

Based on the following recipe (from your original question), using second order approximations, we conclude:

1kg of flour
200g of egg         --  74% water, so 148 g water
150g of sour cream  --  80% water, so 120 g water
300ml water         -- 100% water, so 300 g water         
                                   --------------
                                      568 g water


So this version of the recipe has a bakers percentage of about 57% hydration.  This is a little lower than your original recipe.

In truth, this may not matter so much as a starting point, because you would adjust the dough by feel as well as hydration percentage.

Other effects

While hydration percentage is an important contributing factor to the quality of your loaves, remember, any time you add ingredients other than the basic four (flour, salt, water, yeast), the additional content of the ingredients are going to affect the structure, texture, crust, rise, and flavor of your final product.

Sugars, fats, and eggs will all significantly change the loaf, both by affecting the gluten development, and by influencing how the yeast grows.