I want to see my transmission line as a series RLC circuit
I understand your need, but the solution is not so simple.
There are tools of the "broad band SPICE" type which can exctract an equivalent circuit model from S-parameters.
But let's see how to do that manually:
For your case, I would split the EM model into a "line" piece and a "via" piece.
For the line, we can calculate the corresponding R'L'G'C' elements, or simplify that using Zline = sqrt (L'/C') and extract that from simulation. To get the C', you can simulate an open ended piece of line. To get the L' you can simulate a short (less than lambda/20) length of line that is shorted at the end.
For the via (excluding the line!), depending on frequency we can use a pi model (series L and two shunt C) or see if a series L is good enough. To get the via alone (excluding the line!) from your EM results, you would need reference plane shift which your EM solver might not provide. In that case, you would do the de-embedding yourself, for example in ADS using the S2P de-embedding element.
This is not trivial, but certainly possible.