Table with predefined dimensions and horizontally and vertically centered cells

Your friend in such cases is the command

rule[-5em]{0pt}{10em}

which adds an invisible rule above and below the contents of each cell -- dimensions as per choice

The pros an cons of various types of vertical and horizontal padding are discussed at many places on this site including --

Column and row padding in tables

The new P type of column gives the horizontal and vertical centering which you look for -- with centering for horizontal centering and m{} giving the vertical centering in the command

newcolumntype{P}[1]{>{rule[-5em]{0pt}{10em}centeringarraybackslash}m{#1textwidth}}

The width of each column is defined as a percentage of the text width by simply entering P{0.4} thereby meaning the column will take up 40% of the text width

documentclass[12pt,a4paper]{article}
usepackage[utf8]{inputenc}
usepackage[czech]{babel}
usepackage[T1]{fontenc}
usepackage{amsmath}
usepackage{amsfonts}
usepackage{amssymb}
usepackage{graphicx}


usepackage[total={17cm,25.7cm}, top=2cm, left=2cm, includefoot, bindingoffset=-0.63cm]{geometry}
%usepackage[twoside, hscale=0.88, vscale=0.88, bindingoffset=0cm]{geometry}



usepackage{tikz}
usepackage{array}
usepackage{booktabs,adjustbox}

%
%newcommand{finalcells}[2]{%
%   begingroupsbox0{begin{minipage}{3cm}centering#1end{minipage}}%
%   sbox2{begin{minipage}{3cm}centering#2end{minipage}}%
%   xdeffinalheight{thedimexprht0+dp0+smallskipamountrelax}%
%   xdeffinalheightB{thedimexprht2+dp2+smallskipamountrelax}%
%   ifdimfinalheightB>finalheight
%   globalletfinalheightfinalheightB
%   fiendgroup
%   begin{minipage}[t][finalheight][t]{3cm}centering#1end{minipage}&
%   begin{minipage}[t][finalheight][t]{3cm}centering#2end{minipage}}

newcolumntype{P}[1]{>{rule[-5em]{0pt}{10em}centeringarraybackslash}m{#1textwidth}}
begin{document}
    
%   {setlength{extrarowheight}{3.5 cm}
        %setlength{tabcolsep}{4.25cm}
        
        begin{tabular}{| P{0.4} | P{0.4} |} 
            
            hline
            asdasd  & •  
            hline 
            • & •  
            hline 
            • & •  
            hline 
            • & •  
            hline 
            • & •  
            hline 
            • & •  
            hline 
        end{tabular}
%   }
    
    
end{document}

It is not clear what you like to have. More empty space above/below cell contents? What should happen, if you have longer text in cells, for example if it is break in four lines?

I guess, that the following (much simpler) solution gives what you like to get:

documentclass[12pt,a4paper]{article}
usepackage[total={17cm,25.7cm},
            top=2cm, left=2cm,
            includefoot, bindingoffset=-0.63cm]{geometry}
usepackage[czech]{babel}
usepackage[T1]{fontenc}

usepackage{array, booktabs}
usepackage[column=O]{cellspace} % for additiona vertical space above/below cells contets
    setlengthcellspacetoplimit{22pt}
    setlengthcellspacebottomlimit{22pt}
usepackage{adjustbox}
usepackage{lipsum}

begin{document}
    begin{tabular}{| >{centeringarraybackslash}O{m{8.5cm}} 
                    | >{centeringarraybackslash}O{m{8.5cm}} |}
    hline
asdasd      & lipsum[1][1-3]   
    hline
    •       & •                 
    hline
    •       & •                 
    hline
    •       & •                 
    hline
    end{tabular}
end{document}