Equicalent circuit - RC // RC
Start with the individual series networks: -

$$Z = R + \dfrac{1}{sC} = \dfrac{sCR + 1}{sC}$$

In case you were not sure s = jω.

Now, if you add the two networks as admittances then take the reciprocal you get: -

$$Z_{PARALLEL} = \dfrac{1}{\dfrac{sC}{sCR+1} + \dfrac{sC}{sCR+1}}$$

$$ = \dfrac{sCR +1}{2\cdot sC}$$


  did I miss something with my calculations/ understanding ?


Your understanding was fine but your calculation went wrong somewhere.