The same left and right labels on every tree node - TikZ

I’m am trying to form a tree where every node has a ‘(‘ before the node and a ‘)’ after the node. I understand that this is achievable through something like this:

documentclass{standalone}

usepackage{tikz}

begin{document}
begin{tikzpicture}[sibling distance=10em,
        every node/.style = {shape=circle, draw, align=center}]]
    node[label={left:(}, label={right:)}] {}
    child { node[label={left:(}, label={right:)}] {} }
    child { node[label={left:(}, label={right:)}] {}
            child { node[label={left:(}, label={right:)}] {}
                    child { node[label={left:(}, label={right:)}] {} }
                    child { node[label={left:(}, label={right:)}] {} }
                    child { node[label={left:(}, label={right:)}] {} } }
            child { node[label={left:(}, label={right:)}] {} } };
end{tikzpicture}
end{document}

Giving the following result:

However, this is not ideal and I would rather not have to copy and paste the same code each time (something something maintainability). I have tried placing the label code within the node style, however that doesn’t seem to be supported. I have tried to find a way to create a custom node to which I can assign labels, but I also have struggled to get something like that working / haven’t been able to find anything on it.

For context, I am trying to display a tree representation of a Dyck word where the pre and post numbers after performing DFS represent the indices of ‘(‘ and ‘)’.

Desired code form:

begin{figure}
    begin{tikzpicture}[sibling distance=10em,
            every node/.style = {shape=circle, draw, align=center}]] % <-- some style here for the ()?
        node {}
        child { node {} }
        child { node {}
                child { node {}
                        child { node {} }
                        child { node {} }
                        child { node {} } }
                child { node {} } };
    end{tikzpicture}
end{figure}

documentclass{standalone}

usepackage{tikz}

begin{document}
begin{tikzpicture}[sibling distance=10em,
        ears/.style={shape=circle, draw, align=center,
            label={left:(}, label={right:)}},
        every child node/.style = {ears}]]
    node[ears] {}
    child { node {} }
    child { node {}
            child { node {}
                    child { node {} }
                    child { node {} }
                    child { node {} } }
            child { node {} } };
end{tikzpicture}
end{document}

documentclass{standalone}

usepackage{tikz}

tikzset{dyck/.style={
    draw,
    circle,
    label={left:(},
    label={right:)},
    }
}

begin{document}
begin{tikzpicture}[sibling distance=10em,
        every node/.style = {shape=circle, draw, align=center}]]
    node[dyck] {}
    child { node[dyck] {} }
    child { node[dyck] {}
            child { node[dyck] {}
                    child { node[dyck] {} }
                    child { node[dyck] {} }
                    child { node[dyck] {} } }
            child { node[dyck] {} } };
end{tikzpicture}
end{document}